Question

How many different 4-member committees are possible there must be at least 1 girl?

A. The total number of 4-member committees
B. The total number of 4-member committees with no girls
C. The total number of 4-member committees with at least 1 girl
D. The total number of 4-member committees with only boys

Answer 1

To find the number of different 4-member committees with at least 1 girl, we need to consider different cases and calculate the number of ways to select the girls and boys using combinations.

Step-by-step explanation:

To find the number of different 4-member committees with at least 1 girl, we need to consider the different cases:

1. Case 1: 1 girl and 3 boys
2. Case 2: 2 girls and 2 boys
3. Case 3: 3 girls and 1 boy
4. Case 4: 4 girls

In each case, we can calculate the number of committees by multiplying the number of ways to select the girls and boys. Using combinations, the number of ways to select k items from a set of n items is given by the formula C(n, k) = n! / (k!(n-k)!).

Therefore, the total number of different 4-member committees with at least 1 girl is the sum of the number of committees in each case.