Q3 of 118 Page 17

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.


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