In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?

In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?

Answer Details

To form a committee of 5 from 7 males and 3 females with at least one female:

Choose 1 female from 3: 3C1 ${}^{\mathrm{<br>}}$ = 3

Choose 4 males from 7: 7C4 ${}^{\mathrm{<br>}}$ = 35

Total ways = 3 × 35 = 105

The total number of ways to select the committee is: 105ways.