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Combinatorics

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Counting Words, Every Element Appears at Least Once

COMBIN-SXREKQ

Given a set $X$, a word of length $n$ is a list $a_1a_2\ldots a_n$ where $a_i \in X$. Suppose $X = \{f, u, n\}$. How many words of length 6 are there that use every element of $X$ at least once.

A

243

B

540

C

709