AMC 8 2022 Problem 14

AMC8 2022 年第 14 题

排列与组合★★★☆☆

In how many ways can the letters in

\textbf{BEEKEEPER}

be rearranged so that two or more

\textbf{E}

s do not appear together?

将 BEEKEEPER 中的字母重新排列，使得没有两个或更多的 E 连排在一起，共有多少种排列方式？

正确答案 · Correct Answer

解析 · Solution

Solution 1

All valid arrangements of the letters must be of the form

\textbf{E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}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!=24 ways.

继续练习