00:01
All right, in your question, you're playing a six -card hand from a standard deck of cards, and you want to know what the probability that you would get four jacks and two non -jacks.
00:11
Well, there's only four jacks in a deck.
00:14
So there's four jacks to choose from.
00:21
So what you can think of is that there's only one possible way to get four jacks.
00:35
You have to have all four jacks.
00:36
There's only one way for that to happen.
00:39
But we have these other two cards because we're getting a six -card hand two other cards i'll call them and we don't care what they are okay so we want to figure out how many different ways we can get groups of two cards that is what's called a combination there's 48 cards for us to choose from because we're not going to be choosing from the jacks the four jacks are taken like i said there's only one way to do that but for the two other cards we do 48s c2, which is going to tell us how many different groups of two cards there are out of 48 cards to select from.
01:19
And again, that c stands for what's called a combination.
01:24
Usually the symbol on a calculator is ncr.
01:28
So i'll put that above if you case you need to look for that.
01:33
But 48c2 works out to be 1 ,128 different ways that we could get two different cards.
01:43
Out of the 48 cards that are available.
01:47
We take that and we multiply it to one, since there's only one possible way to get these jacks, so there's basically 1 ,128 hands that could be dealt that would have four jacks.
02:01
That represents your numerator and the probability.
02:07
Now your denominator is how many possible six card hands are there? and we'll do something very similar to this, but since it's just how many are possible...