Solution: 2014 Winter Final - 12
Author: Michiel SmidQuestion
We choose a subset of $\{1,2,3,4,5\}$ uniformly at random. What is the probability that this
subset has size 3?
(a)
4/32
(b)
5/32
(c)
5/16
(d)
4/16
Solution
The total number of subsets of a set with 5 elements is $2^5 = 32$.
The number of ways to choose a subset of size 3 from a set of 5 elements is $\binom{5}{3} = 10$.
The probability of choosing a subset of size 3 is the ratio of the number of favorable outcomes to the total number of outcomes:
$P(\text{subset of size 3}) = \frac{10}{32} = \frac{5}{16}$