2006 AIME I Problems/Problem 4
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 I (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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