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

Hello Clarisse!

Remember, in all of these items, the order of the students doesn't matter.

a) We have to arrange 5 students, from a group of 7 (Hospitality students). This is calculated as:

7!/(5! 2!) = 21

b) Now, we'll have to arrange 3 students, from a group of 5 (Business students). The we'll have to arrange the remaining 2 students, from a group of 7 (Hospitality students). This is calculated as:

5!/(3! 2!) * 7!/*(2! 5!) = 10 * 21 = 210

c) We'll have to calculate the sum of the possibilities of forming committees with:

0 Business students: same as a) = 21

1 Business students: 5! /(4! 1!) * 7!/(4! 3!) = 5* 35 = 185

2 Business students: 5! /(2! 3!) * 7!/(3! 4!) = 10 * 35 = 350

21 + 185 + 350 = 556

Feel free to schedule a class! Best regards!