Question

In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?

Answer 1

We are given that 2 courses are compulsory out of the 9 available courses,
Thus, a student can choose 3 courses out of the remaining 7 courses.
Number of ways = ${}^7{C}_3=\frac{7!}{3!4!}=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}=35$