Question

A resort manager is choosing a committee of four people to discuss employment issues. He'll choose from eight housekeepers, three desk clerks, and five maintenance workers. How many possible committees are there if there have to be at least two housekeepers?

Answer 1

To calculate the number of possible committees with at least two housekeepers, we can use the concept of combinations.

Step-by-step explanation:

To calculate the number of possible committees with at least two housekeepers, we can use the concept of combinations. First, we need to select the two housekeepers from the eight available housekeepers, which can be done in C(8, 2) ways. Then, we can choose the remaining two members from the pool of desk clerks and maintenance workers.

There are three desk clerks and five maintenance workers available. We can select two members from this pool in C(8, 2) ways. Finally, we multiply the number of ways for each step together to get the total number of possible committees with at least two housekeepers.

Total number of committees = C(8, 2) * C(8, 2) = 28 * 28 = 784.