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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- Jan 5th 2011, 10:59 AMprasumword 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

- Jan 5th 2011, 11:23 AMtonybruguier
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 - Jan 6th 2011, 07:47 AMprasum
but how will i get the answer

- Jan 6th 2011, 07:56 AMtonybruguier
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 - Jan 10th 2011, 12:52 AMprasum
can yu give some hint

- Jan 10th 2011, 02:53 AMemakarov
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.

- Jan 10th 2011, 05:08 AMprasum
can yu help me

- Jan 10th 2011, 05:30 AMsnowtea
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?