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Math Help - combination/permutation

  1. #1
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    combination/permutation

    I've done this before like months ago and now I forgot what these mean, so I need someone to explain to me what's going on lol

    Question: How many different 4 letters words can be formed using letters of the word "MISSISSIPPI"

    4 same --- 2 ways
    3 same 1 different --- 2C1 X 3C1 X4!/3! <<I need someone to explain each of them to me ,3 of those ,if the other 3 at bottom are different ,please explain too thanks!
    2 same 2 same --- 3C2 X4!/2!
    2 same 1 diff 1 diff --- 3C1 X 3C2 4!/2!
    1d 1d 1d 1d --- 4!

    Total:176
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  2. #2
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    Re: combination/permutation

    Quote Originally Posted by wong93 View Post
    I've done this before like months ago and now I forgot what these mean, so I need someone to explain to me what's going on lol

    Question: How many different 4 letters words can be formed using letters of the word "MISSISSIPPI"

    4 same --- 2 ways
    3 same 1 different --- 2C1 X 3C1 X4!/3! <<I need someone to explain each of them to me ,3 of those ,if the other 3 at bottom are different ,please explain too thanks!
    2 same 2 same --- 3C2 X4!/2!
    2 same 1 diff 1 diff --- 3C1 X 3C2 4!/2!
    1d 1d 1d 1d --- 4!

    Total:176
    The explanation takes you through how to form 4 letter words with the different possibilities. There are 4 different letters.
    • There are 2 ways to have a four letter word with the same letters (SSSS, IIII).
    • 3 same letters is {2 \choose 1} and 1 different letter is  {3 \choose 1} since there are 3 letters different from the same letters. The multiplier \frac{4!}{3!}=4 takes care of the fact that you could have 4 arrangements as in SSSP, SSPS, SPSS, PSSS.
    • 2 same letters is {3 \choose 2} (i.e. there are three different letters that you can have two of). Again, the \frac{4!}{2!} is a multiplier to include the arragements
    • Can you continue with this logic to understand the rest?


    Hope this helped.
    Last edited by majamin; March 20th 2013 at 12:36 PM.
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  3. #3
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    Re: combination/permutation

    the questions stated that 4 letters word only and i don't need answer for this question ,i need explanation of what is being written there,cause i forgot what are those,thanks anyway
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