Permutations and Combinations- Problem 1

6 6 cards numbered 1 1 to 6 6 are to be lined up in a row. Find the number of arrangements of these 6 6 cards where one of the cards can be removed leaving the remaining 5 5 cards in either ascending or descending order.

Source: American Invitational Mathematical Olympiad(AIME) 2020 2020 - paper 1 1


The answer is 52.

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