I am a tomato ^_^

Out of all the permutations of the letters of the word "tomatoes" , the permutations in which 2nd O is the 5th letter of the word, are \(\dfrac{a}{b}\) times of total. (The ratio of number of these special permutations to the number of all permutations is \(\dfrac{a}{b}\) ) where \(\mathrm{gcd(a,b)}= 1\). Find the value of \(a+b\)

\(\bullet\) This problem is a part of the set Vegetable combinatorics

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