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 ${}^7{C}_3$ ways.

Thus, the required number of ways of choosing the programme

${\Rightarrow }^7{C}_3=\frac{7!}{3!4!}$
$=\frac{7\times 6\times 5}{3\times 2\times 1}$

$=35$