Question

Jones is the chairman of a committee. in how many ways can a committee of 5 be chosen from 10 people given that jones must be one of them?

Answer 1

Since Jones is mandatory, you have 9 people to choose from for the second seat, then 8 for the third, 7 for the fourth, and finally 6 for the fifth.

So your equation is
1(Jones) • 9( possibilities left) •8( possibilities left)• 7( possibilities left)• 6( possibilities left)
Or

1 • 9 • 8 • 7 • 6
=
3,024 possible ways in which a committee of 5 can be chosen from 20 people given that Jones must be one of them.