2022 AMC 8

Complete problem set with solutions and individual problem pages

Problem 14 Medium

In how many ways can the letters in \textbf{BEEKEEPER} be rearranged so that two or more \textbf{E}s do not appear together?

  • A.

    1

  • B.

    4

  • C.

    12

  • D.

    24

  • E.

    120

Answer:D

All valid arrangements of the letters must be of the form

\textbf{E}\underline{\hspace{1.5mm}}\textbf{E}\underline{\hspace{1.5mm}}\textbf{E}\underline{\hspace{1.5mm}}\textbf{E}\underline{\hspace{1.5mm}}\textbf{E}

The problem is equivalent to counting the arrangements of \textbf{B},\textbf{K},\textbf{P}, and \textbf{R} into the four blanks, in which there are 4!=\boxed{\textbf{(D) } 24} ways.

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