In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Question

Philoid · Accepted Answer

Given that a student needs to choose 5 courses out of 9 courses. It is also told 2 courses are compulsory to the student.

It is similar to choosing 3 courses of remaining 7 courses since 2 courses are already chosen.

Let us assume the no. of ways of choosing to be N,

⇒ N = (no. of ways of choosing 3 courses out of remaining 7 courses)

⇒ N = ⁷C₃

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒ N = 35

∴ The no. of ways of choosing 5 courses is 35.