A committee is to consist of three members. If there are six men and four women available to serve on the committee, how many different committees can be formed?

no

.

A dinner menu has 4 different entrees, 4 different sides, and 5 different desserts. How many different dinners consisting of an entree, a side, and a desert can you choose?

336

To find the number of different committees that can be formed, we need to use the concept of combinations.

In this case, we have 6 men and 4 women to choose from, and we need to select 3 members for the committee.

The formula for combinations is given by:

nCr = n! / (r!(n - r)!)

Where n is the total number of items to choose from and r is the number of items to select.

Using this formula, we can calculate the number of different committees that can be formed:

For selecting men:
There are 6 men available, and we need to select 3. So, the number of combinations for selecting men is given by:
6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

For selecting women:
Similarly, there are 4 women available, and we need to select 0 women since we have already selected 3 members from the men. Therefore, the number of combinations for selecting women is given by:
4C0 = 4! / (0! * (4-0)!) = 4! / (0! * 4!) = 1

To find the total number of committees, we multiply the number of combinations for selecting men with the number of combinations for selecting women:
Total number of committees = 20 * 1 = 20

Therefore, there are 20 different committees that can be formed with three members selected from six men and four women.

6*5*4 all men

6*5*4 two men, one woman
6*4*3 one man, two woman
4*3*2 three women

add these up (336)
Is there a simpler way to solve this?