Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2022 AMC 8 Problems/Problem 14"
(→‎Categorized problem)
 
(2 intermediate revisions by 2 users not shown)
Line 11: Line 11:
  
 
~MRENTHUSIASM
 
~MRENTHUSIASM
 +
 +
==Video Solution (A Clever Explanation You’ll Get Instantly)==
 +
https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=1740
 +
~hsnacademy
  
 
==Video Solution by Math-X (First understand the problem!!!)==
 
==Video Solution by Math-X (First understand the problem!!!)==
Line 41: Line 45:
  
 
~harungurcan
 
~harungurcan
 +
 +
==Video Solution by Dr. David==
 +
https://youtu.be/iqjSY6kiEOk
  
 
==See Also==  
 
==See Also==  
 
{{AMC8 box|year=2022|num-b=13|num-a=15}}
 
{{AMC8 box|year=2022|num-b=13|num-a=15}}
 
{{MAA Notice}}
 
{{MAA Notice}}
 +
 +
[[Category:Introductory Combinatorics Problems]]

Latest revision as of 17:35, 4 June 2025

Problem

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

$\textbf{(A) } 1 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 12 \qquad \textbf{(D) } 24 \qquad \textbf{(E) } 120$

Solution

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 $4!=\boxed{\textbf{(D) } 24}$ ways.

~MRENTHUSIASM

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=1740 ~hsnacademy

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/oUEa7AjMF2A?si=sMxdry7U6U_2bPZH&t=2168

~Math-X

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/419vsFnrGeY

~Education, the Study of Everything

Video Solution

https://youtu.be/Ij9pAy6tQSg?t=1222

~Interstigation

Video Solution

https://youtu.be/p29Fe2dLGs8?t=212

~STEMbreezy

Video Solution

https://youtu.be/NmfnoSn3CDg

~savannahsolver

Video Solution

https://youtu.be/c6shf8oma5c

~harungurcan

Video Solution by Dr. David

https://youtu.be/iqjSY6kiEOk

See Also

2022 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_AMC_8_Problems/Problem_14&oldid=249703"