EXAMPLE 1.6.7

Six Democrats and five Republicans are in a jail cell. Either three Democrats or three Republicans will be chosen for a police line-up. How many different line-ups are possible? (We assume that a line-up is determined not only by the people who are chosen, but also by the order in which they are "lined-up.")

A. 990

B. 7200

C. 33

D. 180

SOLUTION

A line-up will consist of either 3 Democrats or 3 Republicans. Thus, the number of line-ups will be the number of 3-Democrat line-ups plus the number of 3-Republican line-ups.

Number of 3-Democrat line-ups:

We are choosing three of the six Democrats and arranging them in order to form a line-up, so the number of outcomes is P(6,3).

Number of 3-Republican line-ups:

We are choosing three of the four Republicans and arranging them in order to form a line-up, so the number of outcomes is P(5,3).

There are 120 different Democrat line-ups and 60 different Republican line-ups, so the total number of line-ups is

120 + 60 = 180