SOLUTION: How many rearrangements of the letters FACEBOOK have the two O's not together?

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Question 981027: How many rearrangements of the letters FACEBOOK have the two O's not together?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
How many rearrangements of the letters FACEBOOK have the two O's not together?

First we calculate the number of distinguishable permutations of FACEBOOK

If the O's were distinguishable as FACEBOoK, the number would be 8!

For we would be able to tell the difference between EBKoAFCO and EBKOAFCo.
But since we cannot tell the O's apart we must divide by 2!

No of distinguishable arrangements of FACEBOOK  = 20160.

From this number we must subtract the number of ways the O's come together.

Then we have the 7 things {F,A,C,E,B,(OO),K} to arrange and they are all
distinguishable.  [Notice that the double O is considered as just one thing.]

So there are 7! ways of arranging those 7 things.

Final answer =  = .

Edwin
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