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
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

Difference between revisions of "2006 AIME A Problems/Problem 4"

 
Line 10: Line 10:
 
== See also ==
 
== See also ==
 
*[[2006 AIME II Problems]]
 
*[[2006 AIME II Problems]]
 +
 +
[[Category:Intermediate Combinatorics Problems]]

Revision as of 09:35, 16 July 2006

Problem

Let $(a_1,a_2,a_3,\ldots,a_{12})$ be a permutation of $(1,2,3,\ldots,12)$ for which

$a_1>a_2>a_3>a_4>a_5>a_6 \mathrm{\ and \ } a_6<a_7<a_8<a_9<a_{10}<a_{11}<a_{12}.$

An example of such a permutation is $(6,5,4,3,2,1,7,8,9,10,11,12).$ Find the number of such permutations.

Solution

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_AIME_A_Problems/Problem_4&oldid=7784"