From a group of 5 Business students and 7 Hospitality students, a committee of 5 members is to be formed to discuss plans for the exhibit. How many committees can be formed given each condition?

Question

a. All are Hospitality students

b. 3 are Business students

c. At most 2 are Business students

Answer 1

Hi Clarissa!

Since you are looking for how many ways to place people in a committee, you will want to use the Combination formula.

For part a, you have 7 possible Hospitality students for a committee of 5, so you will want the combination of 7 choose 5, or 7!/5! (7-5)!

Use the same strategy for b.

For part c, at most 2 are business students means 0, 1, or 2 Business students, which means 5, 4, and 3 Hospitality Students respectively. You will need to calculate all three of these combinations and add the three results together.

For example, 1 Business and 4 Hospitality students would be:

(C 5 choose 1) X (C 7 choose 4). — you multiply since you need both:)