We wish to survey high schools in a particular city.If the city has 22 high schools and we want to select 5 of them, how many unique samples of size 5 are possible?
A) 3,160,080
B) 5,153,632
C) 26,334
D) 2.384 × 1015

Question

Quizplus · Accepted Answer

The number of unique samples of size 5 that can be selected from 22 high schools is calculated using the combination formula, which is $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items (22 high schools) and $k$ is the size of each sample (5 high schools). Plugging in the values, we get $C(22, 5) = \frac{22!}{5!(22-5)!} = \frac{22!}{5!17!} = 26,334$.

We Wish to Survey High Schools in a Particular City