Counting (when used)

Definition

When outcomes are equally likely, P=favorable/total. Counting uses product rule, permutations P(n,k)=n!/(n−k)!, combinations C(n,k)=n!/(k!(n−k)!).

Decide if order matters. Combinations for hands/committees; permutations for sequences.

Inclusion-exclusion handles overcounting unions.

Not every probability problem needs counting — continuous spaces need integrals.

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1.Probability of being dealt 2 aces in a 5-card hand (setup OK if unsimplified).