"Not a run of the mill 20 balls in a bag problem!"

The credit for this problem goes not to me, but I found it very interesting (link to problem included in solutions). I can't see any way to do this without a computer program - so you are allowed to use one to solve it. However, I would be very interested to hear about a solution which does not require the use of a computer program.

The problem

There are a bag of 20 coloured balls: 3 Blue, 4 Pink, 5 Yellow and 8 Green. Pick balls out of the bag without replacement until you have 3 balls of the same colour.

Calculate the probability of those 3 balls being: a) Blue b) Pink c) Yellow d) Green

Let the 4 probabilities you get be B, P, Y, G respectively.

Type into the answer box: \(1000B + (200P)^2 + (100Y)^3 + \frac{100}{G}\)


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