In how many ways can a student choose a programme of 5 courses if 9

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:

There are 9 courses available out of which, 2 specific courses are compulsory for every student.

Therefore, every student has to choose 3 courses out of the remaining 7 courses. This can be chosen in ${ }^{7} \mathrm{C}_{3}$ ways.

Thus, required number of ways of choosing the programme

$={ }^{7} \mathrm{C}_{3}=\frac{7 !}{3 ! 4 !}=\frac{7 \times 6 \times 5 \times 4 !}{3 \times 2 \times 1 \times 4 !}=35$

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