From a group of six men and five women 3 male roles and 4 female roles need to be chosen for the upcoming community play how many different cast lists can be made?

6C3 * 5C4

Thank u Scott :)

To determine the number of different cast lists that can be made, we need to use the concept of combinations.

In this case, we need to choose 3 men from a group of 6 and 4 women from a group of 5.

The number of ways to choose 3 men from a group of 6 is given by the formula:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of men and r is the number of men to be chosen.

Applying this formula, we have:

C(6, 3) = 6! / (3! * (6-3)!)
= 6! / (3! * 3!)
= 6 * 5 * 4 / (3 * 2 * 1)
= 20

Therefore, there are 20 different ways to choose 3 men from the group.

Similarly, the number of ways to choose 4 women from a group of 5 is:

C(5, 4) = 5! / (4! * (5-4)!)
= 5! / (4! * 1!)
= 5 * 4 / (1 * 1)
= 20

Therefore, there are 20 different ways to choose 4 women from the group.

To find the total number of different cast lists, we multiply the number of choices for each category:

Total number of cast lists = Number of ways to choose men * Number of ways to choose women
= 20 * 20
= 400

So, there are 400 different cast lists that can be made for the community play.