Question

a local business club has 7 exclusive board members and 31 General members and how many committees of five members can be chosen so that only general managers are included

Answer 1

We need to choose 5 members from the general only

The number of general members = 31

As the arrangement is not required

So, the number of committees will be:

$31C5=\frac{31!}{(31-5)!\cdot5!}=169,911$

so, the answer will be 169,911 committees