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

[Q]: Problem: the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________ 
Options: a ) 0.45 , b ) 0.4 , c ) 0.55 , d ) 0.05 , e ) 0.6
[A]: c


[Q]: Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 34 ? 
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
[A]: b


[Q]: Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 16 ! 
Options: a ) 8 , b ) 10 , c ) 6 , d ) 14 , e ) 16
[A]:
c