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Math Help - Simplify factorials help!

  1. #1
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    Question Simplify factorials help!

    Please can anyone help me to simplify
    (5n)!/(2n)!(3n)!

    Thanks, this is really bugging me.
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  2. #2
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by Frankler View Post
    Please can anyone help me to simplify
    (5n)!/(2n)!(3n)!

    Thanks, this is really bugging me.
    I could be wrong about this, but I don't know how much simpler this can get...

    You can expand it out and see what cancels.

    \frac{(5n)!}{(2n)!(3n)!} = \frac{(5n)(5n-1)(5n-2)(5n-3)(5n-4)\cdot\cdot\cdot}{[(2n)(2n-1)(2n-2)(2n-3)(2n-4)\cdot\cdot\cdot][(3n)(3n-1)(3n-2)(3n-3)(3n-4)\cdot\cdot\cdot]}
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Frankler View Post
    Please can anyone help me to simplify
    (5n)!/(2n)!(3n)!

    Thanks, this is really bugging me.
    The (complete) gamma function \Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by

    \Gamma(n) = (n-1)!


    So your expression can be stated as

    \frac{\Gamma(5 n+1)}{\Gamma(2n+1) \times \Gamma(3n+1)}
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  4. #4
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    Thanks both of you. I've tried cancelling it, and got rid of the (3n)!, but I don't see how that helps...
    And how do you simplify <br />
\frac{\Gamma(5 n+1)}{\Gamma(2n+1) \times \Gamma(3n+1)}<br />
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  5. #5
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    Quote Originally Posted by Frankler View Post
    Please can anyone help me to simplify
    (5n)!/(2n)!(3n)!

    Thanks, this is really bugging me.
    It's basically
    choose 2n elements from 5n elements

    \binom{5n}{2n}=(5n)_{C_{(2n)}}=\frac{(5n)!}{(5n-2n)!(2n)!}
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  6. #6
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    Yes, that where I started with this problem, but does anyone know how it simplifies??
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  7. #7
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    Quote Originally Posted by Frankler View Post
    Yes, that where I started with this problem, but does anyone know how it simplifies??
    Why are you so determined to try and simplify it?
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  8. #8
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    Just to finish answering a question. Is there no way to simplify it? I'll just leave it then, thanks
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