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Math Help - What formulas do I need?

  1. #1
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    What formulas do I need?

    So I am revising for my maths test resit cos I suck lol but anyway I have this question

    Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.

    I know it's 13! but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.
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  2. #2
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    Re: What formulas do I need?

    Quote Originally Posted by uperkurk View Post
    So I am revising for my maths test resit cos I suck lol but anyway I have this question
    Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.
    I know it's 13! but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.
    The answer depends on how one reads the question. If it means that the suit is one block is that order then \frac{40!}{52!}.

    On other hand it it means the suit can be spread out but in that order then \frac{\binom{52}{13}\cdot 39!}{52!}.
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    Re: What formulas do I need?

    Quote Originally Posted by uperkurk View Post
    So I am revising for my maths test resit cos I suck lol but anyway I have this question

    Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.

    I know it's 13!
    I'm sorry to hear that. Do you not know that a probability is always between 0 and 1?

    but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.
    I think your problem is that you have no idea what the problem is asking. 13! is nowhere near the correct answer.
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    Re: What formulas do I need?

    Well that's frustrating lol... you're right I don't understand half the questions i'm given, I really struggle with maths but I thought the question meant what are the chances, if you kept shuffling the deck over and over that you'd end up with 1 of the suits in full order. Please explain to question so I get what it means thanks.
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    Re: What formulas do I need?

    Quote Originally Posted by Plato View Post
    \frac{\binom{52}{13}\cdot 39!}{52!}.
    That is the correct one because it asks in order, A23456789TJQK but can you read this out to me? How do I even read your answer in english.
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    Re: What formulas do I need?

    Quote Originally Posted by uperkurk View Post
    That is the correct one because it asks in order, A23456789TJQK but can you read this out to me? How do I even read your answer in english.
    Well the final answer is \frac{1}{13!}. WHY?
    Because \frac{52!}{13!} is the number of ways to arrange 52 cards so that one particular suit is in ascending order ace to king. If we want the probability we divide by 52!.
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    Re: What formulas do I need?

    oh I understand it now.... so there is just as much chance that lets say A2K36579Q48J appearing as there is A23456789JQK, I need to ignore the whole suit part of the question and just think of that as 1 combination, and there are 13! different combinations for that suit to be arranged?
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    Re: What formulas do I need?

    Quote Originally Posted by uperkurk View Post
    oh I understand it now.... so there is just as much chance that lets say A2K36579Q48J appearing as there is A23456789JQK, I need to ignore the whole suit part of the question and just think of that as 1 combination, and there are 13! different combinations for that suit to be arranged?
    Actually that is a very good way to look at this particular question.
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