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Discrete Mathematics Level 3

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 \(a+b\)?

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