Six cards problem

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

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There are 6 cards. If one card is removed remaining 5 cards should be in ascending or descending order.

Selecting a card to be removed is equivalent to selecting the 5 cards not to be removed. This can be done in 6C5= 6 ways.

And the missing number can be in any place between, above and below of the 5 cards i.e in 6 positions.

Thus total no. of ways= 6*6=36

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