# You might need to use Bulbapedia just to answer this problem

I will challenge the next gym leader to a 3 vs 3 Pokemon battle.

I have 10 Pokemons all in all. Out of the ten, there are $$x$$ non-fire type Pokemons. The next gym leader has pure Grass types, and surely I may just need three fire type pokemons in my roster to defeat the gym leader.

But with the gym leader seeing that three fire-type Pokemons in my Pokemon roster is a disadvantage, he asked me to draw three pokeballs RANDOMLY instead, from my pool of 10 Pokemons, thus removing the certainty of facing three fire-type Pokemons.

The probability that none of the three Pokemons is a fire-type is 1/120.

I have a higher chance of defeating the Gym leader if I am able to draw even only one fire-type Pokemon. The probability that exactly one of my three randomly chosen Pokemons is a fire-type, is a fraction $$\frac{a}{b}$$ where $$a$$ and $$b$$ are relatively prime positive integers.

What is $$a+b$$?

(Image source: pokecommunity.com)

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