Question

This year, there are nine freshmen, seven sophomores, seven juniors, and nine seniors are eligible to be on a committee. In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.

Answer 1

There are 510,408 ways to choose a dance committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors from the given student population.

Step-by-step explanation:

To calculate the number of ways a dance committee can be chosen, we can use the concept of combinations.

We can choose 2 freshmen from 9, 2 sophomores from 7, 2 juniors from 7, and 2 seniors from 9.

The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of elements and r is the number of elements to choose.

Using this formula for each group, we have:

Freshmen: C(9, 2) = 9! / (2!(9-2)!)

= 36 ways

Sophomores: C(7, 2) = 7! / (2!(7-2)!)

= 21 ways

Juniors: C(7, 2) = 7! / (2!(7-2)!)

= 21 ways

Seniors: C(9, 2) = 9! / (2!(9-2)!)

= 36 ways

To find the total number of ways, we can multiply the number of ways for each group:

36 * 21 * 21 * 36 = 510,408 ways.