Use permutations and combinations to compute probabilities of compound events and solve problems.
Count permutations when order matters
Problem
The three officer roles are distinct, so order matters. Count the assignments using \(8\) choices, then \(7\), then \(6\).
Big Picture
What this problem is really about
Distinct offices make assignments order-sensitive because the same people in different roles form different outcomes. We’ll count the available person for the first role, reduce the pool for each later role, and multiply the three descending counts. Writing the equivalent permutation notation confirms that no person repeats and that role order remains significant.
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