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kevo

  • 2 years ago

How many ways are there to rearrange the letters in the word "MISSISSIPPI" so that the resulting word contains four consecutive letters S? Hint: Think of the string "SSSS" as a new letter

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  1. AbhimanyuPudi
    • 2 years ago
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    8!/(4!)(2!)

  2. kevo
    • 2 years ago
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    Could you please explain abhimanyu?

  3. AbhimanyuPudi
    • 2 years ago
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    Take {S,S,S,S} to be one letter....then you will have 8letters in which there are 4I's and 2P's....So arranging n things in which m are one type and n are of one type is n!/(m!)(n!)

  4. kevo
    • 2 years ago
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    THANKS!!!

  5. kevo
    • 2 years ago
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    hold on though, wouldn't we need to factor in that the S's can be in any particular order, so we have to avoid multiples, yeah?

  6. kevo
    • 2 years ago
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    8!/(4!*4!*2!)?

  7. Ishaan94
    • 2 years ago
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    it won't matter. SSSS is gonna look the same.

  8. Ishaan94
    • 2 years ago
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    so, no permutation for the S group.

  9. kevo
    • 2 years ago
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    So I wouldn't have to take into account the S's? But for the I's and the P's?

  10. Ishaan94
    • 2 years ago
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    because you can have ISSSSI... or IISSSSI... but not SSIISS...

  11. AbhimanyuPudi
    • 2 years ago
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    IMISSSSIPPI and MSSSSIIPIPI are two of the arrangements...here if you take a look, you will find all S's together but I's and P's may be all together or a few together and others seprated or all may be separated...So, I's and P's must be considered for arranging but not S's

  12. kevo
    • 2 years ago
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    OH! I see where this is going. But couldn't you also have ISSSSI and ISSSSI with just the S's rearranged?

  13. AbhimanyuPudi
    • 2 years ago
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    if S's are rearranged the word looks the same but if I's and P's are rearranged, word changes and thats what the question is about..Find the different words formed by reaarrangement

  14. kevo
    • 2 years ago
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    Ahhhhh I see, thank you for your guys' help! I really appreciate it

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