Use permutations and combinations to compute probabilities of compound events and solve problems.
Decode a combination or permutation probability expression
Problem
Interpret \(C(13,2)C(39,3)/C(52,5)\) by identifying the unordered \(2\text{-}\text{from}-13\) and \(3\text{-}\text{from}-39\) favorable categories and the \(5\text{-}\text{from}-52\) sample space.
Big Picture
What this problem is really about
A probability expression can be decoded from the denominator outward. We’ll identify the total outcome type and whether order matters, translate each numerator factor into a category count, check that those counts fill the whole outcome, and combine the constraints into one event description.
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