In combinatorics two basic rules show up often:
Sum rule — you choose one option from several mutually exclusive groups.
Product rule — a choice is made in sequential steps, and each step has its own options.
“Or” usually leads to addition
“And” (step by step) usually leads to multiplication
First identify the structure of the choice, then count
Decide which rule applies.
Pick a drink: 4 juices or 3 teas
4+3
Sum rule: choose one from disjoint options.
=7
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