How many 5-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 both) must be on the committee?

A.) If there are no restrictions, Number of committes possible = 9C5 = 126

b.) If both Jim and Mary must be in the committee, then we are now choosing 3 persons from the remaining 7 people. So the number of committes possible = 7C3 = 35

c.) If either Jim or Mary (but not both) must be on the committe, then there are 7 people availabe and 4 choices to make after taking either Jim or Mary. Also, there are 2 possible ways of choosing either Jim or May.

Theefore, Number of committe possible = 2 (7C4) = 2 (35) = 70