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All the digits of a number are different, the first digit is not zero, and the sum of the digits is 36. There are N × 7! such numbers. What is the value of N?

How should I approach this problem? I know that the number of digits is at maximum 8 because if it were 9 then their sum would be $\sum _{i=1}^9i=45 \gt 36$. However I find it hard to actually count the number of such numbers, what should I do? How shall I think?

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Hint:

The unused digits sum to $9$.

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