Final answer:
To find the number of possible four-person committees with a minimum of 2 women from a group of 6 women and 9 men, we consider three cases based on the number of women on a committee. The total number of such committees is 735.
Step-by-step explanation:
To calculate how many four-person committees can be formed from a group of 6 women and 9 men with the stipulation that there must be a minimum of 2 women on each committee, we can use combinatorics. The committees can have either 2 women and 2 men, 3 women and 1 man, or all 4 women.
Case 1: 2 Women and 2 Men
We select 2 women from the 6 available, and then 2 men from the 9 available.
Number of ways to select 2 women: 15 (using 6 choose 2)
Number of ways to select 2 men: 36 (using 9 choose 2)
Total for Case 1: 540 (15 multiplied by 36)
Case 2: 3 Women and 1 Man
We select 3 women from the 6 available, and then 1 man from the 9 available.
Number of ways to select 3 women: 20 (using 6 choose 3)
Number of ways to select 1 man: 9 (using 9 choose 1)
Total for Case 2: 180 (20 multiplied by 9)
Case 3: All 4 Women
We select all 4 women from the 6 available.
Number of ways to select 4 women: 15 (using 6 choose 4)
Total for Case 3: 15
Adding all the cases together:
Total number of committees: 735 (540+180+15)