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Math Help - [SOLVED] How many six-letter computer passwords are possible?

  1. #1
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    [SOLVED] How many six-letter computer passwords are possible?

    If upper-case and lower-case letters are considered as different letters,how many six-letter computer passwords are possible
    a) with no repeated letters?
    b) with at least one capital letters?

    The right answer is:
    1)19 770 609 664
    2)19 461 693 888

    Would anyone be able to help me with this question?

    Thanks in advance!
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  2. #2
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    Combinations and Permutations

    Hello, this is a problem involving combinations and permutations, now because it involves the arrangement of 6 letter words, we use the permutative formula

    nPr = n!/(n-r)!

    Or in other words, how many different combinations from 52 letters can 6 letter words be made?

    If this doesn't help message back.
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  3. #3
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    Quote Originally Posted by andrew2322 View Post
    Hello, this is a problem involving combinations and permutations, now because it involves the arrangement of 6 letter words, we use the permutative formula

    nPr = n!/(n-r)!

    Or in other words, how many different combinations from 52 letters can 6 letter words be made?

    If this doesn't help message back.
    That answers part (a) (and the answer the OP gives for part (a) is actually wrong - it's the answer for repetition being allowed).

    Part (b) requires clarification on whether or not repetition is allowed. The answer given by the OP is consistent with repetition being allowed: 52^6 - 26^6.

    All this is moot since the OP asked this question at another website and got a correct response. Which is why I marked the thread as Solved. I probably should have closed the thread as well but I thought there might have been some fresh insight ....
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