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

Example 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
Example Output: c

Example Input: Problem: the length of the ribbon was originally 55 cm . it was reduced in the ratio 11 : 7 . what is its length now ?
Options: a ) 6 cm , b ) 12 cm , c ) 35 cm , d ) 44 cm , e ) none of these
Example Output: c

Example Input: Problem: the ratio of flour to water to sugar in a recipe is 10 : 6 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Example Output:
b