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February 20th, 2012, 11:48 AM   #1
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counting problem

Hi,

How many different ways can you arrange the letters of the word "VISITING" such that the letters ing (in all 3! possible cases) are next to each other.
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February 20th, 2012, 01:43 PM   #2
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Re: counting problem

Hello, scream!

I think I've solved it . . .


Quote:
How many different ways can you arrange the letters of the word "VISITING"
such that the letters ING (in all 3! possible cases) are next to each other?







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February 21st, 2012, 11:50 AM   #3
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Re: counting problem

Thanks a lot soroban. I think 6! is not true. Consider the smaller problem for letters of the word "VIIIN" such that IN are next to each other. With your reasoning the number of all possible words should be (4!)(2!)/(3!)=8, but the answer is 18. I think I have found true answer of the original problem. It is 6!-2.5.5!=1920, but I am not sure yet.
Thanks again.
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