Question:
In How many ways can a student chose 5 courses out of 9 courses if 2 specific courses are compulsory for every student?
Solution:
Since every student needs to choose 5 courses out of which 2 are compulsory. So, the student needs to choose 3 subjects out of 7.
No. of ways for choosing 3 subjects out of 7 is ${ }^{7} \mathrm{C}_{3}$
Applying formula ${ }^{n} \mathrm{C}_{r}=\frac{n !}{r !(n-r) !}$ , we get
= 35 ways.