Question

How many 4 person committees are possible from a group of 9 people if

(a) There are no restrictions?
(b) Both Jim and Mary must be on the committee?
(c) Either Jim or Mary(but not boh) must be on the committee?

Answer 1

Assuming there is no order (IE: the jobs aren't specific like President, secretary, etc.) you can use combinations to find the numbers.
A) With no restriction, you have 9 people and choose 4 so 9C4=126
B) With Jim and Mary on, you have two spots filled. That leaves 7 people for the other two, IE: 7C2=21.
C)If Jim is there and not Mary, you have 7C3=35. Ditto if Mary is there and not Jim. Thus you have 35+35=70 total commitees.