How many different committees of 7 people can be formed from a group of 10 people?

Solution:

We have to find the number of ways for a committee of 7 to be chosen from a group of 10 people.

Using combination formula,

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

Here, n = 10 and r = 7

So, \(^{10}C_{7}=\frac{10!}{7!(10-7)!}\)

\(\\^{10}C_{7}=\frac{10!}{7!(3!)}\\=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(7\times 6\times 5\times 4\times 3\times 2\times 1)(3\times 2\times 1)}\\=\frac{10\times 9\times 8}{3\times 2\times 1}\)

= \(\frac{720}{6}\)

= 120

Therefore, there are 120 different committees.

How many different committees of 7 people can be formed from a group of 10 people?

Summary:

There are 120 different committees of 7 people that can be formed from a group of 10 people.