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: four 6 faced dice are thrown together . the probability that all the three show the same number on them is ? 
Options: a ) 1 / 32 , b ) 1 / 216 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
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: a bag contains 6 black and 9 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? 
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5
Output: 


Output: e
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 bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability that out of the two , one is white and one is blue ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
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 bag contains 10 black and 20 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? 
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 3 / 7
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 getting a sum 9 from two throws of dice 
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
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 how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
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: a circular dartboard of radius 1 foot is at a distance of 20 feet from you . you throw a dart at it and it hits the dartboard at some point q in the circle . what is the probability that q is closer to the center of the circle than the periphery ? 
Options: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58
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: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random form this box . the probability that at least one of these is defective is : 
Options: a ) 8 / 19 , b ) 7 / 19 , c ) 10 / 19 , d ) 20 / 19 , e ) 22 / 19
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 the sum of two dice will yield a 8 , and then when both are thrown again , their sum will again yield a 8 ? assume that each die has 7 sides with faces numbered 1 to 7 . 
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49
Output: 


Output: e
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 fair coin is tossed 3 times . what is the probability of getting at least 2 tails ? 
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4
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: a fair coin is tossed 4 times . what is the probability of getting at least 2 tails ? 
Options: a ) 1 / 16 , b ) 1 / 2 , c ) 3 / 16 , d ) 11 / 16 , e ) 3 / 8
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 number is selected at random from the first 40 natural numbers . what is the probability that the number is a multiple of either 2 or 21 ? 
Options: a ) 21 / 40 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 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: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 a for the digits ? 
Options: a ) 30 , b ) 52 , c ) 66 , d ) 68 , e ) 84
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: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose their own dress ? 
Options: a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191
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: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a jack , queen , or king is drawn ? 
Options: a ) 1 / 4 , b ) 1 / 12 , c ) 2 / 13 , d ) 3 / 13 , e ) 3 / 26
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 certain club has 10 members , including jarry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that jarry will be either the member chose to be secretary or the member chose to be treasurer ? 
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Output: 


Output: e