2006 AIME II Problems/Problem 4
Contents
[hide]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.
Solution 2
There are ways to choose 6 numbers from , and then there will only be one way to order them. And since that , only half the combinations will work, so the answer is 12-tuples - mathleticguyyy
See also
2006 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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