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?

Answer 1

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 $^7C_3$ ways. Thus, required number of ways of choosing the programme
$=\space^7C_3=\frac{7!}{3!4!}$

$=\frac{7\times6\times5\times4!}{3\times2\times1\times4!}$
$=35$