Lots-of-LoRAs/task1424_mathqa_probability huggingface dataset:
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a gardener is going to plant 2 red rosebushes and 2 white rosebushes . if the gardener is to select each of the bushes at random , one at a time , and plant them in a row , what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes ? 
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) ½
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ? 
Options: a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30
Output: 


Output: a
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ? 
Options: a ) 15 / 16 , b ) 21 / 32 , c ) 31 / 32 , d ) 63 / 64 , e ) 51 / 64
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: if you throw two dice at a same time . can you find the probability of getting sum as 10 of the two numbers shown ? 
Options: a ) 1 / 16 , b ) 2 / 14 , c ) 1 / 12 , d ) 1 / 19 , e ) 1 / 17
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: in a single throw of a die , what is the probability of getting a number greater than 4 ? 
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Output: 


Output: a
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ? 
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge 
Options: a ) 36 , b ) 2 , c ) 8 , d ) 48 , e ) none of these
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: three coins are tossed . find the probability of at least 1 head and 1 tail ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king or queen ? 
Options: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 7 / 8 probability that task 1 will be completed on time , and a 1 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? 
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? 
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ? 
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 2 / 7 , d ) 10 / 21 , e ) 5 / 11
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ? 
Options: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
Output: 


Output: a
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be odd ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: in lottery , there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ? 
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: how many different ways can 2 students be seated in a row of 8 desks , so that there is always at least one empty desk between the students ? 
Options: a ) 50 , b ) 42 , c ) 24 , d ) 20 , e ) 12
Output: 


Output: b