Competition problem — Combinatorics

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Combinatorics Difficulty 5.1 AIME, harder Find the answer

Let $X$ be as in problem 13. Let $Y$ be the number of ways to order $X$ crimson flowers, $X$ scarlet flowers, and $X$ vermillion flowers in a row so that no two flowers of the same hue are adjacent. (Flowers of the same hue are mutually indistinguishable.) Find $Y$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Problems 13-15 go together. See below.

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