EXAMPLE 1.6.2 SOLUTION

We must choose 3 Representatives and 3 Senators. There are 8 Representatives from whom to choose, so the number of ways to choose 3 of them is C(8,3).

There are 6 Senators from whom to choose, so the number of ways to choose 3 of them is C(6,3).

There are 56 ways to choose 3 Representatives and 20 ways to choose 3 Senators, so according to the Fundamental Coounting Principle the number of ways to choose 3 Representatives and 3 Senators is (56)(20) = 1120.

Do you understand why we used the combination formula (rather than the permutation formula) to obtain the two numbers that were multiplied in this problem?