Use permutations and combinations to compute probabilities of compound events and solve problems.
Find the probability of a compound selection event using permutations or combinations
Problem
Use \(52P_{3}\) total ordered triples and \(4\times~4\times~4\) favorable ace-king-queen triples. Form favorable over total.
Big Picture
What this problem is really about
A required rank in each draw position makes this an ordered without-replacement event. We’ll count all ordered three-card draws with decreasing deck totals, count favorable sequences by the available cards of each required rank, divide compatible counts, and confirm the setup with sequential conditional probabilities.
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