Question

This year, there are eight freshmen, nine sophomores, eight juniors, and ten seniors are eligible to be on a committee. In how many ways can a dance committee of 8 students be chosen?

Answer 1

To solve this problem, we can use the combination formula, which is:

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

where n is the total number of students eligible for the committee, r is the number of students we want to choose, and ! denotes the factorial function.

In this case, we want to choose a committee of 8 students from a pool of 8 freshmen, 9 sophomores, 8 juniors, and 10 seniors. So, the total number of students eligible for the committee is:

n = 8 + 9 + 8 + 10 = 35

We want to choose a committee of 8 students, so r = 8. Therefore, the number of ways we can choose a committee of 8 students is:

35 C 8 = 35! / (8! * (35-8)!) = 35! / (8! * 27!) ≈ 1,121,112 ways

So there are approximately 1,121,112 ways to choose a dance committee of 8 students from the eligible pool.