00:01
All right, we've got number 20.
00:03
Number 20 talks about aces.
00:05
There are a couple of different ways that this problem has been phrased in the past.
00:08
Sometimes they ask you what's the probability of drawing four aces.
00:11
What's the probability of drawing four aces in a row? in this particular question, they're asking, what's the probability of the aces sticking together, right? which means that you wouldn't have to necessarily draw them from the top of the stack of cards.
00:23
They could be in the middle of the stack of cards somewhere, all in a row, all four aces.
00:28
Okay, so that's what we're dealing with right here.
00:29
All right, so let's try to figure this out.
00:32
We've got all four aces next to each other in the deck somewhere.
00:37
So there are, of all the different shuffles that exist, all the different possible permutations, right, of all 52 cards, we're going to have 52 factorial.
00:48
That's just every single possible different way that they could come out.
00:52
Okay.
00:53
And the four aces that are together, let's think of them as like a big block of like four cards.
00:59
So imagine there's like, you know, all these four aces are all in a row together.
01:05
Think of this as being like a unit, right? there's our ordered set of aces.
01:12
Or actually unordered.
01:13
We'll find out in a second.
01:14
Anyway, so there's the group together.
01:16
So we have that.
01:16
And then if you take those four cards and, you know, treat them as a group, then we've only got the rest of the cards, right? which is only like there's a deck of only 49 leftovers.
01:28
Right? so this we have 52, 51, 50, 50.
01:31
And 49.
01:39
So the chunk a is that additional piece...