The Rule of Product

Math 381 Blog # 1

How many shirt and pants combinations can I wear if I have 7 shirts and 5 pairs of pants? This and other questions can be answered by the basic concepts of combinatorics. We will be using something called The Rule of Product. According to Arthur T. Benjamin, “The rule of product states that if an action can be performed by making A choices followed by B choices, then it can be performed A*B ways.”

Let’s look at the shirt and pants problem first. Again, we have 7 shirts (A shirts):

and 5 pairs of pants (B pairs of pants)