Sum rule

Sum rule ( $m+n$ )

If outcome $A$ can be chosen in $m$ ways, $B$ in $n$ ways, and choosing both $A$ and $B$ in one “case” is impossible, then “ $A$ or $B$ ” happens in $m+n$ ways. Phrases like “or…”, “either…”, “in one of mutually exclusive scenarios” signal a sum (after checking $A\cap B=\varnothing$ in the intuitive sense of the problem).

If cases overlap, naive $m+n$ overcounts — you need inclusion–exclusion or another model

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