I am a chilli

You have \(\color{Red}{\textbf{20 distinct red chilies}}\) and \(\color{Green}{\textbf{10 distinct Green chilies}}\).

The number of \(\color{Red}{\text{special red chili powders}}\) you can form is \(\color{Red}{R}\).

The number of \(\color{Green}{\text{special green chili powders}}\) you can form is \(\color{Green}{G}\).

Then the ratio \(\dfrac{\color{Red}{R}}{\color{Green}{G}}\) is equal to \(\dfrac{a}{b}\) where \(a\) and \(b\) are coprime, positive integers, find \(a+b\).

Details and assumptions -

For making a special chili powder, you can at once use exactly \(2\) chilies, and of same color.

\( \color{Red}{\text{Red chili}}+ \color{Green}{\text{Green chili}} \neq\) any of the asked powders.

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


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