Question

A committee must be formed with 2 teachers and 4 students. If there are 9 teachers

to choose from, and 9 students, how many different ways could the committee be
made?

Answer 1

To form the committee, we need to calculate the combinations of teachers and students. There are 4,536 different ways to form the committee.

Step-by-step explanation:

To calculate the number of different ways the committee can be made, we need to use the concept of combinations. The number of ways to choose 2 teachers out of 9 can be calculated as 9 choose 2, denoted as C(9,2). This can be calculated as 9! / ((9-2)! * 2!). Similarly, the number of ways to choose 4 students out of 9 can be calculated as 9 choose 4, denoted as C(9,4). This can be calculated as 9! / ((9-4)! * 4!). Finally, to find the total number of ways the committee can be made, we need to multiply the two combinations together. This can be calculated as C(9,2) * C(9,4).

Substituting the values, we get:

C(9,2) = 9! / ((9-2)! * 2!) = 9! / (7! * 2!) = (9 * 8) / (2 * 1) = 36

C(9,4) = 9! / ((9-4)! * 4!) = 9! / (5! * 4!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126

Now, multiplying the two combinations together:

C(9,2) * C(9,4) = 36 * 126 = 4,536

Therefore, there are 4,536 different ways the committee can be made.