Let U = {1, 2,...,n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with |A| = |B| = k and A ∩ B = ∅. We say that a permutation of U separates A from B if one of the following is true.

• All members of A appear in the permutation before any of the members of B.

• All members of B appear in the permutation before any of the members of A.

How many permutations of U separate A from B?

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