Use permutations and combinations to compute probabilities of compound events and solve problems.
Use the multiplication principle to count outcomes in a multi-step choice situation
Problem
An outfit uses \(\text{one}\) shirt, \(\text{one}\) pair of pants, and \(\text{one}\) pair of shoes. Multiply the independent counts \(3\), \(4\), and \(2\).
Big Picture
What this problem is really about
A complete outfit requires one choice from every independent category. We’ll count possibilities stage by stage, multiply shirt and pants combinations, extend each partial outfit through all shoe choices, and use the multiplication principle to obtain the complete-outcome count.
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