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Math Help - Finding the probability of 7 Trials, All 6 success

  1. #1
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    Finding the probability of 7 Trials, All 6 success

    Suppose I roll a fair dice for 7 times. What is the probability that I will roll all the 6 sides of the dice?

    What I have done is this:
    \left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}

    But is this correct?

    I am not sure if the above is correct because I thought it could be a Negative Binomial distribution too. The 7 throws with 6 sides show up is somewhat daunting and makes the question confusing.
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  2. #2
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    Re: Finding the probability of 7 Trials, All 6 success

    Quote Originally Posted by xEnOn View Post
    Suppose I roll a fair dice for 7 times. What is the probability that I will roll all the 6 sides of the dice?
    What I have done is this:
    \left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}
    But is this correct? I am not sure if the above is correct because I thought it could be a Negative Binomial distribution too. The 7 throws with 6 sides show up is somewhat daunting and makes the question confusing.
    I get one-half your answer.
    The string 1123456 can be arranged in \frac{7!}{2!} ways.
    We can have six times that number to account for the fact each of the six sides can be doubled.
    There are a total of 6^7 possible strings,
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  3. #3
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    Re: Finding the probability of 7 Trials, All 6 success

    Thanks, Plato! You're right! The division of 2! to remove the repeated number during the 7th throw. Thanks!!
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