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arranging numbers 1-12 in a sequence, 12x11x10x...x1 ways

Source: Dutch NMO 2012 p5

September 6, 2019
combinatoricsSequenceProduct

Problem Statement

The numbers 11 to 1212 are arranged in a sequence. The number of ways this can be done equals 12×11×10×...×112 \times11 \times 10\times ...\times 1. We impose the condition that in the sequence there should be exactly one number that is smaller than the number directly preceding it. How many of the 12×11×10×...×112 \times11 \times 10\times ...\times 1 sequences satisfy this condition?
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