Question: Let n be a positive integer. Let A be the set of positive integers less than 210n which are multiples of 6, let B be

Let n be a positive integer. Let A be the set of positive integers less than 210n which are multiples of 6, let B be the set of positive integers less than 210n which are multiples of 10, and let C be the set of positive integers less than 210n which are multiples of 14. Find the number of permutations of 1,2,3,..,210n in which the elements of A U B U C occur in decreasing order, but the other numbers in the permutation may occur in any order.

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