Question

As a freshman, suppose you had to take two of four lab science courses, one of two literature courses, two of three math courses, and one of seven physical education courses. Disregarding possible time conflicts, how many different schedules do you have to choose from?

Answer 1

We have 252 different schedules.

Explanation:

We know that as a freshman, suppose you had to take two of four lab science courses, one of two literature courses, two of three math courses, and one of seven physical education courses.

So from 4 lab science courses we choose 2:

`C_2^4=(4!)/(2!(4-2)!)=6`

So from 2 literature courses we choose 1:

`C_1^2=(2!)/(1!(2-1)!)=2`

So from 3 math courses we choose 2:

`C_2^3=(3!)/(2!(3-2)!)=3\\`

So from 7 physical education courses we choose 1:

`C_1^7=(7!)/(1!(7-1)!)=7`

We get: 6 · 2 · 3 · 7 = 252

We have 252 different schedules.