00:01
Okay, if i deal five cards in a poker fan, a number of ways of doing it will be 52c5.
00:11
We're choosing five cards from the entire pack of 52.
00:16
And that you work out on a calculator.
00:19
On the n, on the ti 84 plus, press the math button on the left.
00:25
The arrow keys go to prob and down to ncr.
00:30
Are and type in 52 c5 and you get the answer 259 8960 in the words when you play poker there are roughly 2 .6 million possible hands you can be dealt so that then is my sample space in this case here for a poker hand and the first one what i want is two jacks so out of 52 c 5 or 2598 960, i want to get 2 jacks.
01:11
So there are 4 jacks in the pack, i want to choose 2 of those.
01:16
So it's 4c2.
01:18
And in the pack we have 48 cards which are not jacks.
01:26
And i want 3 of those to get the 5 card hand.
01:31
So 2 jacks out of 4, 3 non -jacks out of all the non -jacks.
01:37
Or 48.
01:41
So this i work out.
01:45
4c2 i can do manually as faster in the calculator.
01:49
It's 4 factorial, 2 factorial, 2 factorial.
01:54
The n's the r formula.
01:57
It's n factorial, n minus r factorial, r factorial.
02:03
So i have here on top will be 4 times 3 times 2 times 1, 24 divided by 4 is 6 times and then 48 c3 same way as before 48 c3 is 17296 over 2598 960 so this i work out so 17 to 996 over 2 598 960 so this i work out so 17 through 96 times 6 first and divide that by 2598 960 and the answer is 0 .0399298.
03:07
298 so we'll say this is correct to 4 decimal places...