Use permutations and combinations to compute probabilities of compound events and solve problems.
Find the probability of an ordered outcome using permutation counts
Problem
Count \(26P_{3}\) equally likely no-repeat ordered codes. Express the probability of \(\text{one}\) exact code as \(\text{one}\) favorable outcome over that total.
Big Picture
What this problem is really about
An exact code lives in an ordered sample space, because changing positions creates a different outcome. We’ll count all no-repeat codes with a descending product, express that total as a permutation, identify how many codes match every specified position, and form favorable outcomes over equally likely total outcomes.
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