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Problem 1082

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Combinatorics Difficulty 5.0 Find the answer BMO Round 1 · United Kingdom · 2007

The number $916238457$ is an example of a nine-digit number which contains each of the digits $1$ to $9$ exactly once. It also has the property that the digits $1$ to $5$ occur in their natural order, while the digits $1$ to $6$ do not. How many such numbers are there?

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