# 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?

**Solution:**

There are a total of 9 courses, and a student has to select 5 out of which 2 are specific courses that are compulsory.

So we have to find the number of ways in which 5-2 = 3 courses can be selected out of 9-2 = 7 courses.

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ^{n}Cᵣ = n! / [r!(n−r)!]. Using this,

No. of ways of selecting 3 courses out of 7 courses = ⁷C₃

= (7!) / [3! (7-3)!] (Using nCr formula)

= 35

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 Question 9

## 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?

**Summary:**

The number of ways in which a student can choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student is 35