Question

From a pack of 9 cards numbered 1,2,3.......9 , three cards are drawn at random and laid on a table from left to right. What is the probability that the digits are drawn in descending order (by just using permutation)?

Answer 1

The probability is `1/6`.

Explanation:

There are `""_9P_3=9*8*7=504` possible selections to lay three cards from left to right.

However, there are only `""_9C_3=(""_9P_3)/(""_3P_3")=(9*8*7)/(3*2*1)=84` possible selections.

The reason this is `""_9C_3` is because for every selection of three different cards, there is only one possible way for it to be in descending order.

to lay the three cards in descending order. Therefore, the possibility is `84/504=1/6`.