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

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
c

Problem: a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ? 
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
e

Problem: jill ' s favorite number is even and has some repeating prime factors . john is guessing jills favorite number , and the only hint she gives is that 7 is a prime factor . what is johns best guess ? 
Options: a ) 84 , b ) 105 , c ) 54 , d ) 42 , e ) 70

a