In poker, a flush is a hand where all five cards are of the same suit, but not in sequence. A straight is a hand that contains five cards of sequential rank in at least two different suits. A straight flush is a straight that is also a ush (or viceversa), that is, a sequence of five cards all of the same suit. Determine how many poker hands are: 1. Straight flushes 2. Straight 3. Flushes
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- For a straight, pick the face value of the low card (how many choices?) then pick the suit of each card (how many choices?) The suits need not be the same here.
- For a flush, pick the suit (how many choices?) then pick the faces values of the cards (how many combinations?) The face values of the cards need not be consecutive here.
- For a straight flush, pick the face value of the low card, then pick the suit.
Straight flush is most restrive and easiest to quantify. There are 4 suits, and the lowest valued card must be between A(low) and 10. 40 ways to make a straight flush.
Flush -- choose 5 of 13 cards * 4 suits
straight -- 10 cards for the lowest numbered card, 5 cards each can be one of 4 suits.
10*($4^5$)
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One of the answers is
$4 * C(13,5) – 40$
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