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Math Help - word question

  1. #1
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    word question

    how many five letter words can be formed using letters of word MANAGEMENT such that the two alike letters are there then they are always together
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  2. #2
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    You can look at the Wikipedia page on the "Multinomial theorem". In the section "Number of unique permutations of words" it shows you the answer

    https://secure.wikimedia.org/wikiped...tions_of_words

    Tony Bruguier
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  3. #3
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    but how will i get the answer
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  4. #4
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    They work out the example for the word "MISSISSIPPI". You can adapt from it, however, it might be better to try to understand why the formula is correct. I can help you with this if you have specific questions.

    Tony
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  5. #5
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    can yu give some hint
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  6. #6
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    This problem is more complicated than finding the number of permutations of "MISSISSIPPI": first, one counts five-letter words only; second, similar letters must be together.
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  7. #7
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    can yu help me
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  8. #8
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    Letters with multiplicities are (M2, A2, N2, G1, E2, T1).

    How five letter words with 1M 1A 1N 1G 1E?
    How five letter words with 2M's 1A 1N 1G?
    How five letter words with 2M's 2A's and 1N?


    After knowing this, what is one way to count all the possibilities?
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