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Math Help - permutations and combinations

  1. #1
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    Alberta
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    permutations and combinations

    Ok I have been having some trouble with thease questions. Could you show me step by step how to do them?

    1. Solve for n.
    n-1 C 2 = 6

    2. Solve for the variable.
    n P 3 =720
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  2. #2
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    Re: permutations and combinations

    Hello, Twinkie!

    Do you understand the meaning of those symbols?


    \text{1. Solve for }n\!:\;_{n-1}C_2 \,=\, 6

    We have: . \frac{(n-1)!}{2!(n-3)!} \:=\:6 \quad\Rightarrow\quad \frac{(n-1)(n-2)}{2} \:=\:6

    . . (n-1)(n-2) \:=\:12 \quad\Rightarrow\quad n^2 - 3n + 2 \:=\:12

    . . n^2 - 3n - 10 \:=\:0 \quad\Rightarrow\quad (n-5)(n+2) \:=\:0

    Therefore: . n = 5,\;{\color{red}\rlap{//////}}n=\text{-}2




    \text{2. Solve for }n\!:\;_n P_3 \,=\,720

    We have: . \frac{n!}{(n-3)!} \:=\:720 \quad\Rightarrow\quad n(n-1)(n-2) \:=\:720

    . . n^3 - 3n^2 + 2n - 720 \:=\:0 \quad\Rightarrow\quad (n-10)(n^2+7n+72) \:=\:0

    Therefore: . n \,=\,10
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  3. #3
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    Alberta
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    Re: permutations and combinations

    Ok, thankyou for the help!
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