A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

Answer Details

To form a committee of 4 with a chairman, we first need to select a man to be the chairman from the 5 men available. This can be done in 5 ways. Then, we need to select 3 people from the remaining 7 people (4 men and 3 women) to complete the committee. This can be done in 7 choose 3 ways, which is equal to 35. Therefore, the total number of ways to form a committee of 4 with a chairman from a group of 5 men and 3 women is: 5 * 35 = 175 So the correct answer is option (D) 175.