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A password with 8 characters, consisting of Upper case/Lower Case &0-9

  1. Aug 13, 2014 #1
    1. The problem statement, all variables and given/known data


    I am a helping out a friend who is studying Maths at uni, not much help really because I did my degree 10 years ago. I am stuck on a question I was hoping for someone help with the working out:

    A password consist of 8 characters from Uppercase letters, U, lowercase letters L and Digits 0-9, D.

    How many passwords consist of at least one character from U,L & D

    I interpreted this question that it would have to inlcude ULD in the password.

    Anyway I know there are more cases but I think this is wrong anyway - any suggestions will be appreciated.
    2. Relevant equations



    3. The attempt at a solution

    7 D + 1 U/L = 10^7 x 52 x 8c1
    7 U + 1 D/L = 26^7 x 36 x 8c1
    7 L + + 1 D/U = 26^7 x 36 x 8c2
    6 D + 2U = 10^6 X 26^2 x 8c2
    6 D + 2L = 10^6 X 26^2 x 8c2
    6 U + 2D = 26^6 x 10^2 x 8c2 x 2(for L)
    6 U + 2L = 26^6 x 26^2 x 8c2

    Then 1 - (the answer above) is 1.9983 x 10^14
     
  2. jcsd
  3. Aug 13, 2014 #2

    phinds

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    Gold Member
    2016 Award

    Hm ... how about, for example, 4D + 2L + 2U? Does that not meet the criteria? In other words, I think you have specified the MINIMUM amount, not the actual amount.

    Also, with your interpretation of one each, I don't see how 6D + 2U, for example, would meet the criteria.
     
  4. Aug 13, 2014 #3
    I though that 6D + 2U would suit because then I am taking the answer away from 1 so I actually want the opposite of 6D+2U ?
     
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