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Math Help - A Permutation Problem-Urgent

  1. #1
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    A Permutation Problem-Urgent

    We are to solve for n

    Please verify

    P(n,2)=15

    My solution for this problem

    By factoting
    n(n-1) = 15
    n=15 ; n= 16


    Another Problem

    P(n,5) = 20 P(n,3)


    I have no idea how to do it

    Hoping for replies, thanks
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  2. #2
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    Perms and coms

    Hello ImKo
    Quote Originally Posted by ImKo View Post
    We are to solve for n

    Please verify

    P(n,2)=15

    My solution for this problem

    By factoting
    n(n-1) = 15
    n=15 ; n= 16


    Another Problem

    P(n,5) = 20 P(n,3)


    I have no idea how to do it

    Hoping for replies, thanks
    Are you sure the first one isn't C(n, 2)? This would give:

    \frac{n(n-1)}{2!} = 15

    \Rightarrow n(n-1)=30

    \Rightarrow n^2-n-30=0

    \Rightarrow n = 6 or -5

    But n > 0, so the solution is n = 6.

    For the second question:

    n(n-1)(n-2)(n-3)(n-4) = 20n(n-1)(n-2)

    \Rightarrow (n-3)(n-4) = 20

    Can you do it now?

    Grandad
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  3. #3
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    For question number 2

    How many answers should it have?Should it have 2? or 1 only?
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  4. #4
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    Quote Originally Posted by ImKo View Post
    For question number 2

    How many answers should it have?Should it have 2? or 1 only?
    It can have two .... however here there is only 1 solution
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  5. #5
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    Wait here is what I got for question number 2

    n=23 or n=24 Is that correct?Basing from the solution provided

    And what should be the reason for me to remove one of them in order for it to be only one answer?
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  6. #6
    Lord of certain Rings
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    Quote Originally Posted by ImKo View Post
    Wait here is what I got for question number 2

    n=23 or n=24 Is that correct?Basing from the solution provided

    And what should be the reason for me to remove one of them in order for it to be only one answer?
    If we are still talking about "P(n,5) = 20 P(n,3)", then both your answers are wrong.Didnt the problem reduce to solving the quadratic (n-3)(n-4) = 20 ?(As shown by Grandad...)

    (n-3)(n-4) = 20 \Leftrightarrow n^2 -7n -8 = 0. Solve this quadratic...

    Always verify your answers by substituting it back in the original equation and verify if your answer is right...
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  7. #7
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    Oh My mistake!! Sorry

    so using quadratic formula I got

    n = (7 + sqrt17 ) / 2 or n = (7 - sqrt17) / 2

    Is that right?

    Now which should I eliminate
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  8. #8
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    Quote Originally Posted by ImKo View Post
    Oh My mistake!! Sorry

    so using quadratic formula I got

    n = (7 + sqrt17 ) / 2 or n = (7 - sqrt17) / 2

    Is that right?

    Now which should I eliminate
    You should have realised that n is a positive integer therefore:

    1. Your solutions to the quadratic n^2 - 7n - 8 for n are clearly wrong.

    2. The answer to the question Which of the two correct solutions to the quadratic equation should I eliminate? is implied by the word in red .....
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  9. #9
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    Oh! I forgot that the other one is negative, sorry

    Is my last solution correct already?
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  10. #10
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    Quadratics

    Hello ImKo -

    I really think you need to do some work on solving quadratic equations. Your answers using the quadratic formula were incorrect, because you missed a minus sign. But before using the formula, you should always try to factorise - and n^2-7n-8 is one of the easiest quadratic expressions to factorise.

    Can you do it?

    It will look like this: (n - ??)(n + ??)=0

    This will give you two possible values of n, only one of which is appropriate - see mr fantastic's hint.

    Grandad
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  11. #11
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    Sorry I'm a bit careless on solving equations and usually miss the easier approach.. Thanks allot

    so the answer would be n = -1 or n = 8

    then n = 8 ?
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  12. #12
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    Permutations

    Quote Originally Posted by ImKo View Post
    Sorry I'm a bit careless on solving equations and usually miss the easier approach.. Thanks allot

    so the answer would be n = -1 or n = 8

    then n = 8 ?

    Correct!

    Grandad
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