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

Input: Consider Input: Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions ? 
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315

Output: c


Input: Consider Input: Problem: a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is 
Options: a ) 7 / 16 , b ) 7 / 12 , c ) 7 / 19 , d ) 7 / 12 , e ) 7 / 15

Output: e


Input: Consider Input: Problem: a jar contains a mixture of ab in the ratio 4 : 1 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially . 
Options: a ) 12 , b ) 15 , c ) 32 , d ) 20 , e ) 25


Output: c