Question

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?

Answer 1

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