Question

There are 13 female and 12 male teachers. A committee of 3 teachers is chosen at random. How many different combinations of 3 teachers can be chosen, considering both male and female teachers?

1) 78
2) 150
3) 250
4) 390

Answer 1

There are 2300 different combinations of 3 teachers that can be chosen from the given group of 13 females and 12 males.

Step-by-step explanation:

In this problem, we need to find the number of different combinations of 3 teachers that can be chosen from a group of 13 females and 12 males. To solve this, we can use the combination formula:

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

where n is the total number of teachers and r is the number of teachers to be chosen.

Plugging in the values, we have:

C(25, 3) = 25! / (3!(25-3)!)

Simplifying this expression, we get:

C(25, 3) = 25 * 24 * 23 / (3 * 2 * 1) = 2300

Therefore, there are 2300 different combinations of 3 teachers that can be chosen from the given group.