February 20th, 2012, 12:48 PM  #1 
Newbie Joined: Dec 2011 Posts: 15 Thanks: 0  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. 
February 20th, 2012, 02:43 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: counting problem Hello, scream! I think I've solved it . . . Quote:
 
February 21st, 2012, 12:50 PM  #3 
Newbie Joined: Dec 2011 Posts: 15 Thanks: 0  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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