Total no. of courses = 9 No. of compulsory courses = 2 So, the student will choose 3 courses out of 7 courses [non compulsory courses]. ∴ Required no. of ways a student can choose a programme = $\,{}^{7}C_3$ = $\frac{7!}{3!4!}$ = $\frac{7\times6\times5}{6}$ = 35