Maths Olympiad Prep

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Combinatorics Difficulty 5.0 AIME Find the answer

9. A museum has 5 entrances, and each entrance can only allow one person to enter at a time. A delegation of 20 people goes to visit. How many ways are there for them to enter the museum?

A number or a short expression. Spacing and $ signs are ignored.

Solution

9. Each scheme for entering the library corresponds 1-1 to the full permutation of 5 identical white balls and 9 distinct red balls, and the number of permutations is C145P99C_{14}^{5} \cdot P_{9}^{9}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.