From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many combinations of random samples of 4 students can be selected?

Solution:

Given, group of 12 students

We have to select a random sample of 4 students to serve on a university committee.

By using combination formula,

\(C_{n,x}= \frac{n!}{x!(n-x)!}\)

Here, n = 12, x = 4

\(C_{n,x}=\frac{12!}{4!(12-4)!}\)

\(C_{n,x}=\frac{12!}{4!8!}\)

\(C_{n,x}=\frac{12\times 11\times 10\times9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 }{(4\times 3\times 2\times 1)(8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}\)

\(C_{12,4}=\frac{479001600}{967680}\)

\(C_{12,4}=495\)

Therefore, the possible ways of selecting 4 students randomly is 495 combinations.

From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many combinations of random samples of 4 students can be selected?

Summary:

From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. 495 combinations of random samples of 4 students can be selected.