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Homework Help: Math 20: Perms & Combs Help.

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data

    The expression nC5/nC4 can be simplified to:

    2. Relevant equations

    I'm assuming that I'm to use n!/(n-r)!r!

    3. The attempt at a solution

    I attempted to do this:
    n!/(n-5)!5! / n!/(n-4)!4!
    n!/(n-5)!5! x (n-4)!4!/n!
    1/(n-5)!5! x (n-4)!4!
    And I'm stuck after this point. The possible answers are:
    A. 1/5(n-5)
    B. (n-4)/5
    C. 5(n-5)
    D. none of the above.
  2. jcsd
  3. May 29, 2012 #2


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    Hello dancing_math. Welcome to PF !

    1/(n-5)!5! x (n-4)!4! is equivalent to [itex]\displaystyle \frac{(n-4)!\,4!}{(n-5)!\,5!}\ .[/itex]

    You should be able to further simplify [itex]\displaystyle \frac{4!}{5!}[/itex] and [itex]\displaystyle \frac{(n-4)!}{(n-5)!}\ .[/itex]
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