Difference between revisions of "2022 AIME I Problems/Problem 9"

Line 4: Line 4:
  
 
==See Also==
 
==See Also==
{{AIME box|year=2022|n=I|num-b=7|num-a=9}}
+
{{AIME box|year=2022|n=I|num-b=8|num-a=10}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 21:19, 17 February 2022

Problem

Ellina has twelve blocks, two each of red $\left({\bf R}\right),$ blue $\left({\bf B}\right),$ yellow $\left({\bf Y}\right),$ green $\left({\bf G}\right),$ orange $\left({\bf O}\right),$ and purple $\left({\bf P}\right).$ 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 \[{\text {\bf R B B Y G G Y R O P P O}}\]is even. Ellina arranges her blocks in a row in random order. The probability that her arrangement is even is $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

See Also

2022 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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. AMC logo.png