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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