Concept preview

What you will be able to do

1. 01Apply the fundamental counting (multiplication) and addition principles
2. 02Use factorial notation and count arrangements with and without repetition
3. 03Count distinguishable arrangements of items with identical elements

The fundamental counting principle (the multiplication rule) says: if one choice can be made in $m$ ways and, independently, a second in $n$ ways, then the two together can be made in $m \times n$ ways. It chains: 4 shirts and 3 pants give $4 \times 3 = 12$ outfits; a 3-course meal from 3 appetizers, 5 mains, 2 desserts gives $3 \times 5 \times 2 = 30$ meals. Whenever a task is a sequence of independent decisions, multiply the number of options at each stage.