Question

Mrs. Plum’s civics class is going on a field trip to observe the state legislature while it's in session. There are 24 students in the class. The gallery where the class will sit has seating for three people in the front row. In how many ways can Mrs. Plum combine three of the students to sit in the front row if the order is not important

Answer 1

Answer:

2024 ways

Step-by-step explanation:

Because order doesn't matter in this scenario, we can use the binomial function $_nC_k$, where n is the total number of items (students in this case) and k is the number of items we'd like to choose.

This binomial function is equivalent to:

$_nC_k=\frac{n!}{(n-k)!*k!}$, where n! means n * (n - 1) * (n - 2) * ... * 2 * 1

Here, we have $_{24}C_3=\frac{24!}{(24-3)!*3!} =\frac{24!}{21!*3!} =2024$.

Thus, the answer is 2024 ways.

~ an aesthetics lover