Question

Ms. Bell's mathematics class consists of 6 sophomores, 13 juniors, and 10 seniors.

How many different ways can Ms. Bell create a 3-member committee of sophomores
if each sophomore has an equal chance of being selected?

Answer 1

Ms. Bell can create a 3-member committee of sophomores in 20 different ways.

Step-by-step explanation:

To determine the number of different ways Ms. Bell can create a 3-member committee of sophomores, we will use the concept of combinations. The formula for combinations is:

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

In this case, we have 6 sophomores and we need to choose 3 of them. So we will substitute n=6 and r=3 into the formula:

C(6, 3) = 6! / (3! * (6-3)!)

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

Therefore, Ms. Bell can create a 3-member committee of sophomores in 20 different ways.