[MOVED] number of ways to rearrange the letters in....

I have an idea on how to solve this problem, but I want to make sure I am on the right track...

How many ways are there to rearrange the letters of THISISBORING so that no pair of consecutive letters are all the same?

Re: Combinatoric Problem

lladams said:

How many ways are there to rearrange the letters of THISISBORING so that no pair of consecutive letters are all the same?

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Remove the S’s and I’s leaving THBORNG to act like separators. There are eight places to put the three I’s: _T_H_B_O_R_N_G_. That can be done in \(\displaystyle {8 \choose 3} \left( {7!} \right)\) ways [the (7!) comes from rearranging the separators]. Now we have eleven places to put the two S’s. Thus
\(\displaystyle {8 \choose 3} \left( {7!} \right) {{11} \choose 2}\) total ways to do it.

Thanks, that helped greatly!