Question

There are 24 students in a class. The instructor wants to select a five-person committee to plan the annual service project. How many different possible committees are there?

Answer 1

There are 63,504 different possible committees that can be formed from the 24 students in the class.

Step-by-step explanation:

To find the number of different possible committees, we can use the concept of combinations.

Since there are 24 students in the class and the instructor wants to select a five-person committee, we can calculate the number of combinations possible.

The number of combinations of n objects taken r at a time is given by the formula:

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

Substituting the values, we get:

C(24, 5) = 24! / (5! * (24 - 5)!)

Calculating the factorials, we get:

C(24, 5) = 24! / (5! * 19!)

Simplifying, we get:

C(24, 5) = (24 * 23 * 22 * 21 * 20) / (5 * 4 * 3 * 2 * 1)

C(24, 5) = 24 * 23 * 22 * 21 * 4

C(24, 5) = 63,504

So, there are 63,504 different possible committees that can be formed from the 24 students.