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:

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:

2 courses are compulsory out of the 9 available courses. There are 7 more courses.

So, we need to choose 3 courses out of 7 courses.

$\therefore$ Required number of ways $={ }^{7} C_{3}=\frac{7}{3} \times \frac{6}{2} \times \frac{5}{1}=35$

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