Question

How many ways can a teacher select a group of 3 students to sit in the front row if the class has 12 students?

Answer 1

The number of ways a teacher can select a group of 3 students to sit in the front row out of a class of 12 students is 220.

Step-by-step explanation:

In combinatorics, the number of ways to select a group of k objects from a set of n objects is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

For this question, we want to find the number of ways a teacher can select a group of 3 students to sit in the front row out of a class of 12 students. So, we have n = 12 and k = 3:

C(12, 3) = 12! / (3!(12-3)!) = 12! / (3!9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220 ways

Therefore, there are 220 ways for the teacher to select a group of 3 students to sit in the front row.