2022 AMC 8 Problem 14
Attempt Problem 14 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
In how many ways can the letters in BEEKEEPER be rearranged so that two or more E’s do not appear together?
Answer: D
Small hint:
There are E’s and other letters
Big hint:
The four non-E letters must fill the four gaps between the E’s
Solution:
The word has E’s and other letters: B, K, P, and R. To keep no two E’s adjacent, the only possible pattern is with the four non-E letters in the four gaps.
The letters B, K, P, and R can be arranged in those gaps in ways.
Thus, the correct answer is D.
Problem 14 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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- 1998 AMC 8
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