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Math Help - Simplifying Factorials

  1. #1
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    Simplifying Factorials

    Hi Guys,

    Doing some practise papers for my DM final and have come across something I don't quite understand. I didn't do high school math (last time I did any was 8 years ago) so I find this course very challenging/frustrating but enjoyable!

    Question

    Write down:

    \left(\begin{array}{cc}n\\n-3\end{array}\right)

    My answer:

    \frac{n!}{(n-3)!(n-(n-3))!}

    But the actual/final answer should be:

    \frac{n(n-1)(n-2)}{6}

    Can anyone explain how to get this? I understand factorials, but only the basics when variables are involved. Thankyou!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Simplifying Factorials

    It boils down to recognizing:

    n!=n(n-1)(n-2)(n-3)!

    (n-(n-3))!=3!=6
    Last edited by MarkFL; June 12th 2013 at 07:08 AM.
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  3. #3
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    Re: Simplifying Factorials

    I think I need to go bash my head for not seeing this sooner. Thanks Mark, this makes perfect sense!
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  4. #4
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    Re: Simplifying Factorials

    You can borrow my two by four!
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  5. #5
    Forum Admin topsquark's Avatar
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    Re: Simplifying Factorials

    Quote Originally Posted by HallsofIvy View Post
    You can borrow my two by four!
    An infraction for HallsofIvy. A shovel works much better.

    -Dan
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