Counting Principles: Addition and Multiplication Principles

Methods in this video

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1. 1

   Number the crossings: add what points in

   ▶ 0:40

   When to use it: The question shows a map where you can only travel in the direction of the arrows (one-way streets or a one-way grid) and asks how many different routes go from start to finish, with too many routes to trace one by one.

   • Don't trace routes. At each crossing, write how many ways there are to get there from the start; the start gets 1.
   • Each crossing = the sum of the numbers at the crossings whose arrows point into it. Find every incoming arrow first.
   • Work along the arrows, one crossing at a time; the number at the finish is the answer.
2. 2

   Mix and match: one from each, so multiply

   ▶ 3:37

   When to use it: The question has you choose one item from each of two (or more) different groups to make a set (trousers with a shirt, a flavour with a topping) and asks how many sets are possible, or who can make more.

   • Choose one item, then another, one from each group, step after step, so multiply.
   • Draw a grid: one row for each pair of trousers, one column for each shirt; the number of squares is the number of outfits.
   • Watch out: adding counts the items, not the outfits (3 + 4 = 2 + 5, but 3 × 4 = 12 and 2 × 5 = 10).