2022 AMC 8 Problems/Problem 14: Difference between revisions
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==Problem== | ==Problem== | ||
In how many ways can the letters in BEEKEEPER be rearranged so that two or more | In how many ways can the letters in <math>\textbf{BEEKEEPER}</math> be rearranged so that two or more <math>\textbf{E}</math>s do not appear together? | ||
<math>\textbf{(A) } 1 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 12 \qquad \textbf{(D) } 24 \qquad \textbf{(E) } 120</math> | <math>\textbf{(A) } 1 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 12 \qquad \textbf{(D) } 24 \qquad \textbf{(E) } 120</math> | ||
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~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!!!)== | |||
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== | ==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 16:35, 4 June 2025
Problem
In how many ways can the letters in 
be rearranged so that two or more 
s do not appear together?
Solution
All valid arrangements of the letters must be of the form ![\[\textbf{E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}E\underline{\hspace{3mm}}E}.\]](http://latex.artofproblemsolving.com/3/e/c/3ecf6e61439838584cdc342894a7e76208755b5c.png)
The problem is equivalent to counting the arrangements of 
and 
into the four blanks, in which there are 
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!!!)
~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
~savannahsolver
Video Solution
~harungurcan
Video Solution by Dr. David
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. Error creating thumbnail: Unable to save thumbnail to destination
