# Probability problem: Picking consecutively and in ascending order $5$ from $52$ numbered cards

Let's say we have $52$ cards numbered from $1$ to $52$. We consecutively draw $5$ of them, without replacement and without any preference to their order that comes out. What's the probability of drawing those 5 cards in ascending order? (For example: $5$, $12$, $34$, $40$, $51$, with exactly that order.)

What I know is: there are $\binom {52}{5}$ different ways to pick 5 cards from 52. All the rest looks quite complicated...

• They are as likely to come out in increasing order as in any other possible order... – Lord Shark the Unknown Mar 4 '18 at 13:33

## 2 Answers

It's simply the chance that any $5$ different numbers, whether they are picked out of $52$, or $5200$, or whatever, are in ascending order, i.e. $1$ in $120$

Hint:

For $5$ distinct numbers there are $5!=120$ orders.

Only one of them is ascending.

• and each is equally likely – Ned Mar 4 '18 at 14:09
• @Ned In the case that the OP presents: yes. But that is for him to find out. It is not a part of my hint :-). – drhab Mar 4 '18 at 14:16