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

Problem: if x and y are both odd prime numbers andx < y , then how many different positive integer factors does 2 xyhave ? 
Options: a ) 3 , b ) 4 , c ) 6 , d ) 12 , e ) 8
e

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
a

Problem: the ratio of the number of females to males at a party was 1 : 2 but when 5 females and 5 males left , the ratio became 1 : 3 . how many people were at the party originally ? 
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34

c