Question

In an experiment involving a treatment applied to 5 test subjects, researchers plan to use a simple random sample of 5 subjects selected from a pool of 7 available subjects. How many different random samples are possible?

Answer 1

Solution:

The number of ways to select 5 from 7 (when order does not matter) is;

$\begin{gathered} ^7C_5=\frac{7!}{(7-5)!5!} \\ \\ ^7C_5=\frac{7\times6\times5!}{2!\times5!} \\ \\ ^7C_5=21 \end{gathered}$

ANSWER: 21 ways