2. Assume that you play poker with six-card hands. (A straight has all six cards in a row; as in standard poker, aces are high or low and there is no wrap-around. A flush has all six cards in the same...
2. Assume that you play poker with six-card hands. (A straight has all six cards in a row; as in standard poker, aces are high or low and there is no wrap-around. A flush has all six cards in the same suit. (Use combinatorics)
(f) How many six-card hands contain a straight?
Homework Answers
Calculating the straight flush as;
To have a straight flush the hand must consist of all six cards being of the same suit and all in numerical order. There are 12 possible sequences: A – 6, 2 – 7, … , 11 – K, and 12 – A. Since there are 4 suits, then the number of straight flushes possible is just 12 * 4 = 48, with the highest four (each a straight flush 12 – A of one of the four suits) being royal flushes.
So, the straight would be as followed:
There are 12 sequences and 4 choices in that particular card at each rank, hence, the possible no. of ways are 46= 4096 ways.to choose card at each sequence.
Number of six-card hands contain a straight= 12* 46 - 48 = 49,104.
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just （xiii）thanks
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just xiii thanks
(xi) How many different 5-card poker hands can be dealt from a regular 52-card (xii) How many of these hands contain no aces? (xii) How many contain a aces, for a-0 to 4? (xiv) How many contain all cards of the same suit? deck?
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