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

Problem: two family reunions are happening at the taj hotel , the oates reunion and the hall reunion . all 150 guests at the hotel attend at least one of the reunions . if 70 people attend the oates reunion and 52 people attend the hall reunion , how many people attend both reunions ? 
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 28
e

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 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 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 ) 340 , b ) 380 , c ) 472 , d ) 528 , e ) 630

d

