In this task, you need to provide the correct option for a given problem from the provided options.

Q: Problem: a certain university will select 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 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 ) 150 , d ) 165 , e ) 315

A: c
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Q: Problem: there are 76 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 ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36

A: a
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Q: Problem: the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ? 
Options: a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322

A:
e
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