From a pack of 9 cards numbered 1-9, 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?

I know the answer is $\frac{1}{6}$ but am unsure how to get to it. Thanks!

Oct 16, 2017

$\frac{1}{6}$

Explanation:

The number of cards in the pack is irrelevant - they just need to be distinct numbers.

Whichever $3$ cards are drawn will consist of $3$ distinct numbers with exactly $1$ way to order in descending order.

The total number of different possible orders of the $3$ cards drawn is 3! = 3 * 2 * 1 = 6, since there are $3$ choices for the first card, $2$ for the second and one for the third.

So the probability of drawing the cards in descending order is:

1/(3!) = 1/6