In how many ways can a committee of 3 people be selected from a group of 5 men and 4 women if at least one man and one woman must be included in the committee?

To determine the number of ways a committee of 3 people can be selected from a group of 5 men and 4 women, we need to consider the condition that at least one man and one woman must be included in the committee.

Step 1: Select one man and one woman Since we need to include at least one man and one woman, we can choose one man from the group of 5 men in 5 ways, and one woman from the group of 4 women in 4 ways.

Step 2: Select the third member After selecting one man and one woman, we need to choose the third member of the committee. We can select this member from the remaining pool of 8 people (4 men and 3 women). Therefore, we have 8 options for the third member.

Step 3: Calculate the total number of ways To calculate the total number of ways, we multiply the number of options from each step. So, the total number of ways to form the committee is 5 * 4 * 8 = 160.

Therefore, there are 160 different ways to select a committee of 3 people from a group of 5 men and 4 women, where at least one man and one woman must be included.