00:01
So we're looking to make a straight out of a 52 card deck and five card poker.
00:10
And we wouldn't find that probability.
00:14
So we need to find the total number of ways we can get five cards dealt out of 52 cards.
00:19
And that's given as 52 choose five.
00:26
And as a formula, this becomes 52 factorial.
00:31
Divided by five factorial times 52 minus five quantity factorial.
00:44
And we turn this through a calculator, and this ends up being 2 ,598 ,960.
01:01
Now how many of these ways give us a straight? that's going to give us a probability.
01:11
It's supposed to a total hands here.
01:18
Now we're going to look at the straight.
01:21
Well, let's think about what a straight is.
01:25
A straight is any of these 13 cards in a row.
01:31
So you could have two.
01:35
And we're going to, normally ace is above king.
01:40
So you can have two, three, four, five, six.
01:43
That's a straight.
01:43
You could have 8, 9, 10, jack, queen.
01:49
You could have 9, 10, or excuse me, 10, jack, queen, king, ace.
01:57
And that would be a straight.
01:59
So how many ways can these, can we get at these? i don't want to list them.
02:02
I don't think anyone would like to list them all up.
02:05
It's a waste of time, but we have the probability, or do we have the ability to count these using this type of, this, this, probably combination formula.
02:15
So let's think about this.
02:16
We can start starting with two as the lowest going up to ace.
02:32
This is just the way to see it.
02:34
We get five cards.
02:37
And so we could start anywhere in here, like two up to six, three, up to seven, four up to eight.
02:48
We could list those out.
02:49
That's not too cumbersome.
02:51
In fact, there's 10 ways to do it.
02:53
There's two to six.
02:54
We could do three to seven.
02:58
We could do five, four to it...