Problem:
Let be a permutation of for which
An example of such a permutation is . Find the number of such permutations.
Solution:
Because is less than each of the other numbers, . Choose any five numbers of the remaining to fill the first five positions. Their order is then uniquely determined. The order of the remaining six numbers which fill the last six positions is also uniquely determined. Thus the number of such permutations is the number of choices for the first five numbers, which is .
The problems on this page are the property of the MAA's American Mathematics Competitions