Question

From 6 women and 4 men, a committee of 3 is to be formed, including at least 2 women. In how many ways can this be done?

Answer 1

To form a committee of 3, including at least 2 women, from 6 women and 4 men, there are 240 possible ways to do so.

Step-by-step explanation:

To form a committee of 3, including at least 2 women, from 6 women and 4 men, we will consider two scenarios:

1) The committee consists of 2 women and 1 man.

2) The committee consists of 3 women.

For the first scenario, we have 6 choices for the first woman, 5 choices for the second woman, and 4 choices for the man. This gives us a total of 6 * 5 * 4 = 120 possibilities for the first scenario.

For the second scenario, we have 6 choices for the first woman, 5 choices for the second woman, and 4 choices for the third woman. This gives us a total of 6 * 5 * 4 = 120 possibilities for the second scenario.

Adding the possibilities from both scenarios, we have 120 + 120 = 240 possible ways to form the committee. Therefore, there are 240 ways to form the committee of 3 with at least 2 women.