00:01
So we want to know the probability that our five -card poker hand contains cards of five different kinds but does not contain a flush or a straight.
00:10
Well, first, we get all possible combinations of five cards from a deck of 52.
00:15
That is, the five combination of 52 cards.
00:22
All possible five -card combos.
00:29
Next, we want to know how many five -card hands we can possibly get that contain cards of five different kinds.
00:35
But do not contain a flush or straight.
00:38
Well, by the product rule, all five card hands that contain five different cards, different kinds of cards are the five combination of 13 cards because we first assign the five kinds of cards, and then we multiply this by four to the fifth power because we assign a face to each card.
01:02
And this is equal to 13 factorial over five factorial times 8 factorial, and that's equal to, oh, and then we multiply this by 4 to the 5th, and this is equal to 1 ,013 ,1 ,317 ,88.
01:25
And we subtract from this number all possible straights and all possible flushes.
01:32
Well, we can get, by exercise number 17, we can get 10 ,000 ,000, we can get 10 ,000, 2 ,240 possible straits from a deck of 52 cards...