The Counting Principle

You have 3 shirts and 4 pairs of pants. How many outfits can you make? You could draw them all out — but there's a faster way. For each of the 3 shirts you can pair any of the 4 pants, so it's 3 × 4 = 12. Whenever a task happens in stages, you multiply the choices at each stage. That single idea counts passwords, phone numbers, and restaurant menus.