A 3×3 grid is to be filled with the digits 1 through 9 (each used exactly once). How many ways can the first row be filled so that its entries are in increasing order from left to right?
Enter an integer
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We need to choose which 3 of the 9 digits go in the first row; the increasing-order requirement means there is exactly one arrangement for each choice. So the answer is (39)=3!⋅6!9!=84.