00:01
If you choose five cards from a 52 card deck, what is the probability of getting two red and three black? well, the first thing we need to do is figure out how many ways you can get five cards.
00:12
Since order doesn't matter, we're going to do a permutation of 52 things choosing five at a time.
00:19
That's going to be 52 factorial over 52 minus 5 factorial.
00:28
And that will simplify down to 52 factorial over 52 factorial.
00:33
47 factorial.
00:35
Now we need to know how many ways we can get two red and three black.
00:39
Well, let's see about the red.
00:40
That's going to be a permutation of 26 things taking two at a time because there's only 26 red cards.
00:47
So that's going to be 26 factorial over 26 minus 2 factorial, which will be 26 factorial over 24 factorial.
00:56
For the black, there's 26 black cards.
00:59
We want to choose three at a time...