EXAMPLE 1.6.3 SOLUTION

We must choose an all-female pilot/co-pilot team, and also choose an all-male pilot/copilot team. To choose the all female pilot/co-pilot team, we must choose 2 women from the set of 12 women. This is not a combination problem, however, because such a team is determined not only by which two people are chose, but also by which person is designated "pilot" and which person is designated "co-pilot." Thus, the number of all-female pilot/co-pilot teams is P(12,2), which is the number of ways to choose and arrange two people from a set of 12 people.

P(12,2) = 132

Likewise, since there are 8 male aviators from whom to choose, the number of ways to choose an all-male pilot/co-pilot team is P(8,2).

P(8,2) = 56

There are 132 all-female pilot/co-pilot teams and 56 all male pilot/co-pilot teams, so the number of ways to choose an all-female team and an all-male team is (132)(56) = 7,392.