00:01
Okay, 52 cards and the poker hand is five cards.
00:04
Let's work out first, a sample space.
00:09
Now we're choosing 52 cards, choosing five.
00:16
So 52 c5, 52 choose five.
00:20
It's a combination.
00:21
There's no order to a hand of cards.
00:23
And this i can work out one of two ways.
00:27
The formula for ncr, 52 factorial, over 47, factorial.
00:33
Phi factorial.
00:37
That's a bit tedious.
00:39
The best way is a ti84 plus calculator.
00:43
Press the math button on the left.
00:45
With the arrow p.
00:46
Select prob.
00:48
Go down to ncr.
00:51
Press enter.
00:52
I'm just type in 52 c5.
00:57
And we get 2 ,596 ,960 possible.
01:05
Poker hands.
01:07
So about 2 .6 million poker hands are possible.
01:12
Now the first question says the chance of getting a pair of aces.
01:20
So p of pair of aces.
01:27
Sample space 52 c5.
01:32
Now there are four aces in the pack.
01:38
I want two of them so it's four choose two, four c two.
01:43
Now what exactly? pair of aces.
01:47
I want three, i want four.
01:49
So that means there are 48 cards left, which are not aces in the pack.
01:56
I want two of those.
01:58
So that's my answer.
02:00
4c2 times 48 c2 over 52c5.
02:05
That's not correct because i need three cards not two here.
02:12
So it's going to be 48 c3.
02:18
So two aces and three non aces...