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

Problem: what is log 3 ( 4 ) log 4 ( 5 ) . . . log 80 ( 81 ) ? 
Options: a ) 1 , b ) 4 , c ) 81 , d ) log 80 243 , e ) e 81
b

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
c

Problem: in what ratio must rice of rs . 25 per kg be mixed with rice of rs . 12 per kg so that cost of mixture is rs . 20 per kg ? 
Options: a ) 8 : 5 , b ) 5 : 8 , c ) 20 : 25 , d ) 12 : 20 , e ) 25 : 12

a