In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
Given that we need to find no. of ways of choosing 5 courses out of 9 courses if 2 courses are compulsory.
This is similar to choosing 3 subjects out of the remaining 7 subjects as 2 subjects are compulsory.
Let us assume the total no. of ways of choosing courses is N.
⇒ N = No. of ways of choosing 3 subjects out of 7 subjects.
⇒ N = 7C3
We know that ,
And also n! = (n)(n – 1)(n – 2)......2.1
⇒
⇒
⇒
⇒ N = 35
∴ The total no. of ways of choosing 5 subjects out of 9 subjects in which 2 are compulsory is 35 ways.