3.3 Counting with Bijections

Counting Practice

  1. Suppose for a bank account, you must create a PIN of 5 numbers (0-9). How many possible PINs are there?

    Exercise 1

    There are 10 choices for each of the 5 digits of the PIN. By the product rule, this means there are \(10^5\) or 100000 possible PINs.

  2. You can wear a shirt or a tank top, and shorts or pants. You have 3 colors of shirts, 2 colors of tank tops, 4 colors of shorts, and 4 colors of pants. How many different outfits can you make?

    Exercise 2

    Using the sum rule, you have 3+2=5 choices of tops and 4+4=8 choices of bottoms. Then using the product rule, we can pair a top and a bottom in 5\(\cdot\)8=40 ways.