Use permutations and combinations to compute probabilities of compound events and solve problems.
Find the probability of an unordered selection using combinations
Problem
Count favorable hands by taking \(2\) of \(13\) hearts and \(3\) of \(39\) nonhearts, then divide by all \(5\text{-}\text{card}\) hands from \(52\).
Big Picture
What this problem is really about
A card hand is an unordered group, so numerator and denominator should use the same combination model. We’ll count all five-card hands, build favorable hands from the required hearts and the remaining nonhearts, multiply those category counts, and divide by the full sample space.
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