The counting principle, step by step

Four shirts and three pairs of shorts make twelve outfits, not seven.

The question

3 frames, 2 wheels and 4 colors. How many different bikes can you make?

3 frames, 2 wheels and 4 colors. How many different bikes can you make?

324
3×2=6
6×4=24
  1. Each of the 3 frames can go with every one of the 2 wheels, so the choices multiply — they do not add.
  2. First two stages: 3 × 2 = 6.
  3. Then the 4 colors: 6 × 4 = 24.

How it works.

  1. 01

    Each of the 3 frames can go with every one of the 2 wheels, so the choices multiply — they do not add.

  2. 02

    First two stages: 3 × 2 = 6.

  3. 03

    Then the 4 colors: 6 × 4 = 24.