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?
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.