If the letters of the word "METROPOLITAN" are arranged together,what is the probability that neither 2 T's nor 2 O's are adjacent to each other?

Total words which can be formed using the letters of the word METROPOLITAN = 12!/(2!)(2!)
When both T are together then the number of words would be, 11!/2!
When both O are together, the number of words would be 11!/2!
However, in the above cases there will be a repetition. The cases where both T's as well as both O's are together have been counted twice. So we have to remove such cases. i.e. 9!
So, cases without repetition will be 2*11!/2 -9!
Hence the required probability would be 1 - (11!-9!)/12!/4 = 1 - 4*11!/12! + 9!*4/12! = 1 - 1/3 + 1/330
2/3 + 1/330
= 221/330