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Thread: A question related to Permuation and Combination

  1. #1
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    Question A question related to Permuation and Combination

    (b) A computer password, which must contain 6 characters, is to be chosen from the following
    10 characters:


    Symbols ? ! *
    Numbers 3 5 7
    Letters W X Y Z


    Each character may be used once only in any password. Find the number of possible passwords
    that may be chosen if
        (i) there are no restrictions, [1]


        (ii) each password must start with a letter and finish with a number, [2]


        (iii) each password must contain at least one symbol. [3]


    For no iii) each password must contain at least one symbol, I did 3 x 7 x 6 x 5 x 4 x 3 + 3 x 2 x 7 x 6 x 5 x 4 + 3 x 2 x 1 x 7 x 6 x 5 , is this correct?
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  2. #2
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    Re: A question related to Permuation and Combination

    A question.
    I have a question about quartiles. Can I organize from lowest to highest cualitatives variables through a weight assigned to them?
    For example
    John 4
    Alex 3
    Mary 2
    Bob 1 and so if i have a sample: 3 3 3 3 3 1 1 1 2 2 2 2 2 4 4 , can I find the quartiles yet I find for example Q2= 2,5? Thank you
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    Re: A question related to Permuation and Combination

    can we get post #2 moved to it's own thread?
    Thanks from Zhen64
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    Re: A question related to Permuation and Combination

    Quote Originally Posted by Zhen64 View Post
    (b) A computer password, which must contain 6 characters, is to be chosen from the following
    10 characters:
    Symbols ? ! *
    Numbers 3 5 7
    Letters W X Y Z
    Each character may be used once only in any password. Find the number of possible passwords
    that may be chosen if
        (i) there are no restrictions, [1]
        (ii) each password must start with a letter and finish with a number, [2]
        (iii) each password must contain at least one symbol. [3]
    The notation $^N\mathcal{P}_k$ is the permutation of $N$ taken $k$ at a time.

    iii) $^{10}\mathcal{P}_6-^8\mathcal{P}_6$ That is the total possible minus the number of strings containing no symbols.

    @
    romsek, if it were posted in discrete mathematics I could move it. But for now tell Topquark
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    Re: A question related to Permuation and Combination

    Quote Originally Posted by Plato View Post
    The notation $^N\mathcal{P}_k$ is the permutation of $N$ taken $k$ at a time.

    iii) $^{10}\mathcal{P}_6-^8\mathcal{P}_6$ That is the total possible minus the number of strings containing no symbols.

    @
    romsek, if it were posted in discrete mathematics I could move it. But for now tell Topquark
    do you mean

    $^{10}\mathcal{P}_6 - ^{7}\mathcal{P}_6$ ?

    There are 3 symbol characters

    (I see that you do, as it produces the correct answer)
    Last edited by romsek; Sep 21st 2017 at 03:31 PM.
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    Re: A question related to Permuation and Combination

    Quote Originally Posted by romsek View Post
    do you mean
    $^{10}\mathcal{P}_6 - ^{7}\mathcal{P}_6$ ?
    There are 3 symbol characters
    (I see that you do, as it produces the correct answer)
    Thank you, you are correct for some reason I did not count the $*$ as a symbol.
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    Re: A question related to Permuation and Combination

    Hello, thanks for the solution .

    But, I did this and i got a much lower value? 3 x 7 x 6 x 5 x 4 x 3 (one symbol) + 3 x 2 x 7 x 6 x 5 x 4 (two symbol) + 3 x 2 x 1 x 7 x 6 x 5 (three symbol)
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    Re: A question related to Permuation and Combination

    Quote Originally Posted by Zhen64 View Post
    Hello, thanks for the solution .
    But, I did this and i got a much lower value? 3 x 7 x 6 x 5 x 4 x 3 (one symbol) + 3 x 2 x 7 x 6 x 5 x 4 (two symbol) + 3 x 2 x 1 x 7 x 6 x 5 (three symbol)
    Your calculation does give a lower number which is not correct.
    You have counted the number of strings begin with one, two, or three symbols.
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    Re: A question related to Permuation and Combination

    Oh okay, thanks !
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    Re: A question related to Permuation and Combination

    Quote Originally Posted by Zhen64 View Post
    Oh okay, thanks !
    Another way to do it is to choose the items you will use, then permute them. It would look like this:

    Exactly 1 symbol: $\dbinom{3}{1}\dbinom{7}{5}$
    Exactly 2 symbols: $\dbinom{3}{2}\dbinom{7}{4}$
    Exactly 3 symbols: $\dbinom{3}{3}\dbinom{7}{3}$

    Add that together and multiply by the number of permutations of the six chosen characters:

    $\left[ \dbinom{3}{1}\dbinom{7}{5} + \dbinom{3}{2}\dbinom{7}{4} + \dbinom{3}{3}\dbinom{7}{3} \right] 6! = 146,160$

    You can also use this for a similar formula to what Plato arrived at:

    $\left[ \dbinom{10}{6} - \dbinom{7}{6} \right] 6! = 146,160$
    Last edited by SlipEternal; Sep 22nd 2017 at 07:21 AM.
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    Re: A question related to Permuation and Combination

    Thanks alot.
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