instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 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 ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315
answer:
d

question:
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 18 boys and 42 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
answer:
c

question:
Problem: there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89
answer:
d