Using the digits 1, 2, 3, 4, 5, 6, 7, 8 we can form 8! (= 40320) 8-digit numbers in which the eight digits are all distinct. For

Question

Using the digits 1, 2, 3, 4, 5, 6, 7, 8 we can form 8! (= 40320) 8-digit
numbers in which the eight digits are all distinct. For 1 ≤ k≤ 40320,
let a denote the kth number if these numbers are arranged in
increasing order.
12345678, 12345687, 12345768, ..., 87654321;
That is, a₁ = 12345678, a2 = 12345687,..., a40320 = 87654321. Find
a2009-a2008
9

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