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

[lladams]

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?

 

[pka]

Re: Combinatoric Problem

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

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.

 

[lladams]

Thanks, that helped greatly!