Moving Colour Balls

You have a basket of 1000 balls with 3 different colors with equal amount (assuming they will in equal amount). In how many moves you will get the balls of all colors like one red one green one blue, that it will sure you have all colors balls, then in how many attempts you will find that triplet.

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You first pull out the ball let it be Red
Now there may be a chance that balls you are pulling out are all same red colours, this will take 333 moves, than you will get next colour, let it be green, now the same can happen with the green balls so it will take at max more 333 moves to get to the next colour, so you will have a total of 2*333 moves in worst scenario.

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