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Math Help - pleasehelp. permutations and combinations

  1. #1
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    pleasehelp. permutations and combinations

    The number of arrangements of 2n+2 different objects taken n at a time is to the number of arrangments of 2n different objects taken n at a time as 14:5. Find the value of n.

    If 2nPn = 8.(2n-1)P(n-1), find the value of n

    the P refers to the formula in permutations and combinations that is nPr = n!/(n-r)!

    i dont understand how to solve these questions. some help is greatly appreciated. thankyou =D
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  2. #2
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    Hello, flyinhigh123!

    You're expected to know the formula for Permutations
    . . and be able to handle factorials.


    (1) The ratio of the number of arrangements of 2n+2 different objects taken n at a time
    to the number of arrangments of 2n different objects taken n at a time is 14:5.
    Find the value of n.
    2n+2 objects taken n at a time: . _{2n+2}P_n \:=\:\frac{(2n+2)!}{(n+2)!}

    2n objects taken n at a time: . _{2n}P_n \:=\:\frac{(2n)!}{n!}

    The ratio is: . R \;=\;\frac{\dfrac{(2n+2)!}{(n+2)!}} {\dfrac{(2n)!}{n!}} \;=\;\frac{(2n+2)!}{(n+2)!}\cdot\frac{n!}{(2n)!} \;=\;\frac{(2n+2)!}{(2n)!}\cdot\frac{n!}{(n+2)!}

    And we have: . \frac{(2n+2)(2n+1)}{(n+2)(n+1)} \;=\;\frac{14}{5} \quad\Rightarrow\quad 5(2n+2)(2n+1) \;=\;14(n+2)(n+1)

    . . which simplifies to: . n^2 - 2n - 3 \:=\:0 \quad\Rightarrow\quad (n+1)(n-3) \:=\:0 \quad\Rightarrow\quad n \:=\:-1,3


    Therefore: . \boxed{n \:=\:3}

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  3. #3
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    thankyou for your help soroban =D i realli appreciate your clear explaining and solution
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