00:01
Hello everyone, we are given in a poker game five cards are dealt.
00:05
Five cards are dealt from his 10 .52 card deck has been well shuffled.
00:13
And we have to find in the first part how many five card hands are possible.
00:18
So for this, we know from the 52 cards, we select only five cards.
00:27
So, 52 factorial over 5 .5 cards.
00:30
52 minus 5 is 47 factorial we get 52 into 51 into 50 into 409 into 48 into 47 factorial over 5 into 4 into 3 into 2 into 1 into 47 factorial now cancel these this 10 5 12 12 and and 17, we get 2598960.
01:12
Now, in the second part, we have to find what is the probability that you are dealt two pairs.
01:23
And for this we know 52 c5 over that is we let it be.
01:34
M over n so for the value of m we get 13 c2 into 4 c2 into 11 c1 into 4 c1 we get 13 into 12 into 11 factorial over 11 factorial into 2 into 1 into 4 into 3 into 2 factorial over 2 factorial into 2 into 1 into 11 into 4 now cancel these and here 6 cancel this we get 13 into 6 into 44 we get 1 2 3 double 5 2 so the probability will be 1 2 2 double 5 2 over total total 259, sorry, 98, here 2599 -9 -960.
02:44
We get 0 .0 .047.
02:48
And now the third part, in the third part we have to find the probability that you are delta three of a kind, three of a kind or 4 of a kind.
03:06
Now we have to solve this by 3 of a kind means 13c1 into 4c3 into 12c2 into 4c2 into 4c1.
03:22
We have to solve this 13 into 4c1 into 4c1.
03:33
2 into 1 into 12 into 11 10 factorial cancel 2 into 1 into 4 into 4 we get after solving we get 5 4 9 1 2 and this is 3 of a kind now we have solved 4 of a kind 4 of a kind we get 13 c1 into 4 c4 into 12 c2 into 12 c2 into 12 c2 into 4c 1.
04:05
To solve this we get 13 into 1 into 12 into 11 10 factorial cancer 2 into 1 into 4.
04:19
So we get 13 into 6 into 11.
04:24
6 .15.
04:26
Now the values adding these probability is adding these to 54912 plus 624 over total 2598960.
04:45
We get triple 536 over 2598960.
04:52
We get 0 .0213...