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Math Help - poker hand question

  1. #1
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    poker hand question

    I have a small problem

    I read that the there are 10x(4^5) possibilities for a straight (royal and straight flush included)

    But I thought that there were 10x(20x16x12x8x4) possibilites

    My highest card can be 5,6,7,...,K
    So i have 10 possibilities for the highest card

    Now I want to draw a straight 1,2,3,4,5
    I have 20 possibilities for the first one:1 till 5 and there are 4 suits
    for example I draw 1(spades), then I have 16 possibilities for the next card (4 suits and 4 cards).
    What is wrong with my thinking?

    Thanks guys
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  2. #2
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    In a straight C_1 is the 'low' card and C_5 is the high card.
    There are 10 values for C_1: Ace to ten.

    There are 4 suits possible for C_1.
    The same can be said of each C_i ,\;\; 0\le i \le 5

    So 10(4^5).
    Last edited by Plato; October 7th 2008 at 08:02 AM.
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  3. #3
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    I understand that, but what is wrong with my reasoning
    that there should be 20x16x12x8x4(x10) possibilities?
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  4. #4
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    Quote Originally Posted by kuntah View Post
    I understand that, but what is wrong with my reasoning
    that there should be 20x16x12x8x4(x10) possibilities?
    Divide your answer by (5!).
    \frac{20x16x12x8x4(x10)}{5!} = 10(4^5)
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