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?9664124120

To determine the number of ways a committee of 3 people can be selected from a group of 5 men and 4 women, while ensuring that at least one man and one woman are included, we can use the principle of combinations.

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 4 men and 3 women. Therefore, we have 7 individuals to choose from.

Step 3: Calculate the total number of ways To calculate the total number of ways, we multiply the number of choices from each step. In this case, we have 5 choices for the first man, 4 choices for the first woman, and 7 choices for the third member. Therefore, the total number of ways to form the committee is:

5 * 4 * 7 = 140

So, there are 140 different ways to select a committee of 3 people from a group of 5 men and 4 women, while ensuring that at least one man and one woman are included.