a committee of five is going to be selected from a group of twenty people. How many different committees are possible if one person is the chair and the rest are general members?

Answer 1

There are 20 choices for the chair person.

The rest is (19 choose 4) = 19! / (4!*15!) = 19*18*17*16 / (4*3*2*1)

= 19 * 6*17*4 / 2 <--- 4 cancels 16; 3 cancels 18

= 19 * 3 * 17 * 4

= 19 * 17 * 12

= 3876

3876 * 20 = 77520