Difference between revisions of "2022 AIME I Problems/Problem 9"
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| − | . | + | == Problem == |
| + | Ellina has twelve blocks, two each of red <math>\left({\bf R}\right),</math> blue <math>\left({\bf B}\right),</math> yellow <math>\left({\bf Y}\right),</math> green <math>\left({\bf G}\right),</math> orange <math>\left({\bf O}\right),</math> and purple <math>\left({\bf P}\right).</math> Call an arrangement of blocks even if there is an even number of blocks between each pair of blocks of the same color. For example, the arrangement | ||
| + | <cmath> {\text {\bf R B B Y G G Y R O P P O}}</cmath>is even. Ellina arranges her blocks in a row in random order. The probability that her arrangement is even is <math>\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AIME box|year=2022|n=I|num-b=7|num-a=9}} | ||
| + | {{MAA Notice}} | ||
Revision as of 20:19, 17 February 2022
Problem
Ellina has twelve blocks, two each of red 
blue 
yellow 
green 
orange 
and purple 
Call an arrangement of blocks even if there is an even number of blocks between each pair of blocks of the same color. For example, the arrangement
![\[{\text {\bf R B B Y G G Y R O P P O}}\]](http://latex.artofproblemsolving.com/b/c/3/bc3599e5e45a96be60bf9673adcbec71e3da44cc.png)
is even. Ellina arranges her blocks in a row in random order. The probability that her arrangement is even is 
, where 
and 
are relatively prime positive integers. Find 
.
See Also
| 2022 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
