2006 AIME II Problems/Problem 4
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Problem
Let 
be a permutation of 
for which
An example of such a permutation is 
Find the number of such permutations.
Solution
Clearly, 
. Now, consider selecting 
of the remaining 
values. Sort these values in descending order, and sort the other 
values in ascending order. Now, let the selected values be 
through 
, and let the remaining be 
through 
. It is now clear that there is a bijection between the number of ways to select values from and ordered 12-tuples 
. Thus, there will be 
such ordered 12-tuples.
See also
| 2006 AIME II (Problems • Resources) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
