By poker_boy | 4 Comments
Last updated: Saturday, April 12, 2008 | 141 Views Tags: ace, cards, game of poker, many different ways
This week’s question is a good one. Let’s have a look:
Question: How many different ways are there to draw a hand of five cards, in a game of poker, that consists of an ace, a two, a three, a four, and a five of any suit?
Answer: Actually, the above answers are incorrect.
We have 5 cards and 4 suits.
Let's, say we draw the cards in the following order:
Ace, 2,3,4,5
There are 4 suits. So there 4 ways we could draw an Ace first; 4 ways we could draw a 2, 2nd, etc. And so there are 4×4x4×4x4 = 1024 ways of drawing the cards in the above order. However the cards can be drawn in any order, so we have to multipy 1024 by the number of ways the five cards could be ordered when they are drawn. The number of ways the 5 cards could be ordered is 5 factorial (i.e 5!) = 5×4x3×2x1=120. So the number of ways of drawing a hand consisting of the 5 specified cards, in any suit and in any order = 1024×120 = 122,880
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4 comments
Astaroth
April 12, 2008
Well first off there are 4 suits so would take 4 times 52 for the cards in the deck, and divide that by 13 one for each card and then multiply that answer by 5 for the 5 cars you need.
April 12, 2008
Is this five card stud or five card draw? If it is stud then four.
April 13, 2008
If you are looking for a straight but not a flush:
since there are 4 suits each number has 4 ways it can come up. so there are 4*4*4*4*4=1024 ways to draw the hand.
If you are looking for the Probability, it is different.
April 13, 2008
1024
there are 4 aces, 4 1s , 4 2s….etc,
select one from 4 cards, 4 ways
do that for ace, 1, 2, 3, 4.
that will make it (4)x(4)x(4)x(4)x(4)=1024