In this task, you need to provide the correct option for a given problem from the provided options.
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Question: Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? 
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100

Answer: e


Question: Problem: a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? 
Options: a ) 216 , b ) 212 , c ) 214 , d ) 210 , e ) 120

Answer: a


Question: Problem: in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ? 
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8

Answer:
a