The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 as its largest number?  Choose the correct choice from the following answers:
A) 1/2
B) 1/4
C) 1/8
D) 1/16
E) 1/32
The set S has 2^5 = 32 subsets.   The number 5 is in half of these subsets.   Of the remaining 16 subsets, 4 is an element in 8 of them.   Of the remaining 8 subsets, 3 is an element in 4 of them.   Thus 3 is the largest number in 4 subsets of S.   The probability that 3 is the largest number is 4/32 = 1/8.   The answer is 1/8.
<result>C</result>
The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 as its largest number?