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Math Help - Need help solving for 'n': P (n,5) = 42 x P(,3)

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    Need help solving for 'n': P (n,5) = 42 x P(,3)

    Solve for n
    P (n,5) = 42 x P(,3)


    .. This is from a grade 12 Data Management course that I am taking online! Other people have tried to help me on a different forum, but I still don't know what to do!
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  2. #2
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    Quote Originally Posted by cnmath16 View Post
    Solve for n
    P (n,5) = 42 x P(,3)


    .. This is from a grade 12 Data Management course that I am taking online! Other people have tried to help me on a different forum, but I still don't know what to do!
    I assume by P(,3) you meant P(n, 3). I assume that the notation represents permutations. You should know a basic formula which allows the equation to be written as

    \frac{n!}{(n-5)!} = 42 \cdot \frac{n!}{(n-3)!}

    \Rightarrow \frac{1}{(n-5)!} = 42 \cdot \frac{1}{(n-3)!}

    \Rightarrow (n-3)! = 42 (n-5)!


    Now you have three choices:

    Option 1: Guess and check. When you get to n = 10 you'll have the answer.


    Option 2: By definition of the factorial, the equation can be written as

    (n-3)(n-4)(n-5)! = 42 (n-5)!

    \Rightarrow (n-3)(n-4) = 42

    \Rightarrow n^2 - 7n + 12 = 42 \Rightarrow n^2 - 7n - 30 = 0 \Rightarrow (n-10)(n+3) = 0.

    Therefore n = 10 (the negative solution is rejected).


    Option 3: Note that 42 =  7 \cdot 6. Therefore (n-3)! = 7 \cdot 6 \cdot (n-5)!. This suggests that the left and right hand sides are equal to 7!. Hence n = 10. Check it ..... Correct.
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