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Math Help - Password Combinations

  1. #1
    Junior Member
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    Password Combinations

    Im slighty confused on how to calculate this.

    Password must have length between 6 and 8.
    Each password contains at least 1 digit [0-9].
    Other characters either upper case or lower case.

    So we have 62 different possiblities in each position, am i correct?

    im thinking something like 62^6 + 62^7 + 62^8.
    or 62! / 8! + 62! / 7! + 62! / 6!.

    Please help me!
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  2. #2
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    Lexington, MA (USA)
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    Hello, kurac!

    Password must have length between 6 and 8.
    Each password contains at least 1 digit [0-9].
    Other characters either upper case or lower case.

    So we have 62 different possiblities in each position, am i correct? . Yes!

    Consider the 6-character passwords.

    With no restrictions, there are: . 62^6 possible passwords.

    But the password must contain at least one digit.
    We must eliminate the passwords with no digits (all letters).
    . . There are: . 52^6 passwords which have no digits.

    Hence, there are: . 62^6 - 52^6 six-character passwords
    . . which contain at least one digit.


    Similarly, there are:
    . . 62^7 - 52^7 seven-character passwords with at least one digit
    . . 62^8 - 52^8 eight-character passwords with at least one digit.

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  3. #3
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    . * *

    So the result of above is my answer?

    Thanks.
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  4. #4
    Junior Member
    Joined
    Mar 2009
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    Maths Helper, can you please also help me out with the question below?


    How many binary strings of length 10 starts with 0 bit and ends with two 11 bits.


    So, This is what ive done thus far.

    0XXXXXXX11.

    X can be either 1 or 0.

    So, 10! / 7! 3! is what i have come up with.
    But my problem is i havnt considered that each X can take 1 or 0.

    So how to I do this?
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