Question

Samantha must include 1 English class, 1 Algebra class, and 1 Biology class in a schedule. There 3 English teachers, 4 Algebra teachers, and 2 Biology teachers. How many different schedules are possible?

Answer 1

To solve this problem, we make use of the formula of combination.

nCr = n! / r! (n – r)!

where n is the total number of subject teachers and r is the number of subjects r = 1

For the English class n = 3

3C1 = 3! / 1! (3 – 1)! = 3

For the Algebra class n = 4

4C1 = 4! / 1! (4 – 1)! = 4

For the Biology class n = 2

2C1 = 2! / 1! (2 – 1)! = 2

The total number of different schedules would be the product of the three combinations:

total combinations possible = 3 * 4 * 2

total combinations possible = 24