I am a tomato ^_^

Probability Level 5

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 ab\dfrac{a}{b} times of total. (The ratio of number of these special permutations to the number of all permutations is ab\dfrac{a}{b} ) where gcd(a,b)=1\mathrm{gcd(a,b)}= 1. Find the value of a+ba+b

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

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