Question

In how many ways can a committee of 5 men and 4 women be chosen from a group of ‘10’ women and ‘10’ men?

Answer 1

Given:

There are a group of ‘10’ women and ‘10’ men

We will find the number of ways to choose a committee of 5 men and 4 women

We will use the combinations to solve the problem:

The general formula of the combinations is:

`^nC_r=(n!)/((n-r)!\cdot r!)`

First, we will find the number of ways to choose 5 men from 10 men

So, the number of ways =

`^(10)C_5=(10!)/((10-5)!\cdot5!)=(10!)/(5!\cdot5!)=252`

Second, we will find the number of ways to choose 4 women from 10 women

So, the number of ways =

`^(10)C_4=(10!)/((10-4)!\cdot4!)=(10!)/(6!\cdot4!)=210`

Finally, the total number of ways will be =

`^(10)C_5*^(10)C_4=252*210=52,920`

So, the answer will be 52,920