Use permutations and combinations to compute probabilities of compound events and solve problems.
Find the probability of getting an exact category breakdown in an unordered selection
Problem
Count favorable hands by taking \(2\) of \(13\) hearts and \(3\) of \(13\) clubs, then divide by all \(5\text{-}\text{card}\) hands from \(52\).
Big Picture
What this problem is really about
An exact suit breakdown is built from simultaneous category requirements inside an unordered hand. We’ll count the required heart groups and club groups separately, multiply them to form favorable hands, divide by all five-card hands from the full deck, and verify that the category counts fill every card position.
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