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Math Help - permutation 3

  1. #1
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    permutation 3

    1. How many 3-letter arrangements are there of the letters of the word CANADA?
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  2. #2
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    Quote Originally Posted by william View Post
    1. How many 3-letter arrangements are there of the letters of the word CANADA?
    If the word were C A_1 N A_2 D A_3 how many ways would there be?
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  3. #3
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    Quote Originally Posted by Plato View Post
    If the word were C A_1 N A_2 D A_3 how many ways would there be?
    If I use 1 A it will be 4!=24

    2A's it'll be 9

    and 3A's it'll be 1

    so which of these are correct?
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  4. #4
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    NO!
    You did not answer the question. With the subscripts there are six different letters. Now answer.
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  5. #5
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    Quote Originally Posted by Plato View Post
    NO!
    You did not answer the question. With the subscripts there are six different letters. Now answer.
    if we consider the numbers the A's as different letters it's 6!=720 there are 6 ways the A's can be arranged (3!) so 720/6=120?
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  6. #6
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    Quote Originally Posted by william View Post
    if we consider the numbers the A's as different letters it's 6!=720 there are 6 ways the A's can be arranged (3!) so 720/6=120?
    GREAT By George he got it.

    How many ways can you arrange "MISSISSIPPI"?
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  7. #7
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    Quote Originally Posted by Plato View Post
    GREAT By George he got it.

    How many ways can you arrange "MISSISSIPPI"?
    I'm guessing you take 11! ( number of letters in the word ) over 4!( 4s's) 4!(4i's) and 2!(2p's)

    so \frac{11!}{4!4!2!} is what I'm trying to say, but I am having trouble computing this in my calculator
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  8. #8
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    Quote Originally Posted by william View Post
    I'm guessing you take 11! ( number of letters in the word ) over 4!( 4s's) 4!(4i's) and 2!(2p's)
    so \frac{11!}{4!4!2!} is what I'm trying to say, but I am having trouble computing this in my calculator
    CORRECT!
    See how much one can learn if answers are not just passed out.
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  9. #9
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    Quote Originally Posted by Plato View Post
    CORRECT!
    See how much one can learn if answers are not just passed out.
    Absolutely, I prefer you giving me hints rather then giving me the answers, and I appreciate it. Thanks for your time!
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  10. #10
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    Quote Originally Posted by Plato View Post
    GREAT By George he got it.

    How many ways can you arrange "MISSISSIPPI"?
    I just checked the answer in the back of the book and it says 34?
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  11. #11
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    permutation

    Most of the answers at the back of the textbook are wrong.
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  12. #12
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    Quote Originally Posted by william View Post
    If I use 1 A it will be 4!=24

    2A's it'll be 9

    and 3A's it'll be 1

    so which of these are correct?
    This is actually correct! and the answer in your book is correct!

    Splitting it up into three different cases

    for 1A is is 4!=24

    2A's 3*3=9
    (Ex.DAA)

    3A's=1
    (Ex. AAA)

    Thus using the additive principle associated with permutations add all three cases together: \boxed{24+9+1=34}<br />
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