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The E's In BEEKEEPER (2022 AMC 8 P14)

Source:

January 25, 2022
AMC 82022 AMC 8

Problem Statement

In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 24<spanclass=latexbold>(E)</span> 120<span class='latex-bold'>(A)</span> ~1\qquad<span class='latex-bold'>(B)</span> ~4\qquad<span class='latex-bold'>(C)</span> ~12\qquad<span class='latex-bold'>(D)</span> ~24\qquad<span class='latex-bold'>(E)</span> ~120\qquad