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
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