In how many ways can a committee of 4 be chosen from a group of 8 people?

Solution:

We have to find the possible number of ways for a committee of 4 to be chosen from a group of 8 people.

Using combination formula,

\(^{n}C_{r}=\frac{n!}{r!(n-r)!}\)

Here, n = 8 and r = 4

So, \(^{8}C_{4}=\frac{8!}{4!(8-4)!}\)

\(^{8}C_{4}=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(4\times 3\times 2\times 1)(4\times 3\times 2\times 1)}\)

\(^{8}C_{4}=\frac{8\times 7\times 6\times 5}{4\times 3\times 2\times 1}\)

\(^{8}C_{4}=\frac{56\times 30}{24}\)

\(^{8}C_{4}=\frac{56\times5}{4}\)

= 14(5)

= 70

Therefore, there are 70 ways of choosing 4 people for a committee from a group of 8 people.

In how many ways can a committee of 4 be chosen from a group of 8 people?

Summary:

In 70 ways can a committee of 4 be chosen from a group of 8 people.