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Math Help - Permutations/Combinations

  1. #1
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    Permutations/Combinations

    If upper-case and lower-case letters are considered as different litters, how many six-letter computer passwords are possibile with no repeated letters?

    I thought it was 52 pick 6, but its not, why wouldn't it be 52x51x50x49x48x47?
    Explanation would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by peekay View Post
    If upper-case and lower-case letters are considered as different litters, how many six-letter computer passwords are possibile with no repeated letters?
    I thought it was 52 pick 6, but its not, why wouldn't it be 52x51x50x49x48x47?
    You are correct the answer is 52\cdot 51\cdot 50\cdot 49\cdot 48 \cdot 47.
    But that is not fifty-two choose (pick) six: \binom{52}{6}=\frac{52!}{(6!)(46!)}.
    The second is a combination, whereas the first is permutation.
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  3. #3
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    Isn't 52 pick 6 the same as 52x51x50x49x48x47?

    If you punch both into your calculator you get the same answer
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  4. #4
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    Quote Originally Posted by peekay View Post
    Isn't 52 pick 6 the same as 52x51x50x49x48x47?
    Absolutely not!
    Forget your calculator!
    Learn some basic mathematics.
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  5. #5
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    Learn some basic mathematics?...

    52 pick 6 = 52! / (52-6)!
    = 52! / 46!
    correct?
    52!/46!
    is the same as saying 52x51x50x49x48x47
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  6. #6
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    Quote Originally Posted by peekay View Post
    Learn some basic mathematics?...
    52 pick 6 = 52! / (52-6)!
    = 52! / 46!
    correct?
    52!/46!
    is the same as saying 52x51x50x49x48x47
    Absolutely wrong!
    Fifty-two choose (pick is a crude way to put it) six is:
    \binom{52}{6}=\frac{52!}{(6!)(46!)}=\frac{52\cdot 51\cdot 50\cdot 49\cdot 48\cdot 47 }{6\cdot 5\cdot 4\cdot 3\cdot 2 \cdot 1}

    Why have you not learned the definitions involved in these questions?
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  7. #7
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    It's not choose, its pick.

    Pick refers to permutations while Choose refers to combinations. Pick is way different than choose.

    I have several examples in my textbook and its gives me the formula
    nPr = n! / (n-r)!

    Heres an example:

    In a card game, each player is dealt a face down "reserve" of 13 cards that can be turned up and used one by one during the game. How many different sequences of reserve cards could a player have?

    Solution
    Here, you are taking 13 cards from a deck of 52.

    52Pick13 = 52! / (52-13)!
    =52!/39!
    =52x51x50x...x41x40
    =3.9543x10^21


    Straight from the textbook
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  8. #8
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    Good grief! Those math-education folks have struck again.
    This distinction goes against 75 years of tradition.
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