Use permutations and combinations to compute probabilities of compound events and solve problems.
Count permutations when order matters
Problem
For five distinct books, multiply the available positions \(5\times~4\times~3\times~2\times~1\) and express the permutation count using factorial notation.
Big Picture
What this problem is really about
When all objects are distinct and every position matters, the available choices decrease one position at a time. We’ll multiply those counts, recognize the descending product as a factorial, evaluate it, and confirm that reordering the same books creates a different arrangement.
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