Question

Ms. Bell's mathematics class consists of 15 sophomores, 9 juniors, and 6 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

To find the number of ways to create a 3-member committee of sophomores, we need to use the combination formula. The number of ways to choose r items from a set of n items is given by:

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

where n! means n factorial, or the product of all positive integers up to and including n.

In this case, we have 15 sophomores to choose from, and we want to choose 3 of them. Therefore:

C(15, 3) = 15! / (3! * (15-3)!) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455

So there are 455 different ways that Ms. Bell can create a 3-member committee of sophomores.

Step-by-step explanation: