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ur logic is to choose any 1 b ball and then 2 balls from 8 balls.
but u r including many cases repeatedly.
e.g. Let the b balls be b1, b2, b3.
suppose u r choosing both b1 and b2. then it will fall under 2 categories: either u choose b1 and 2 other balls or u choose b2 and 2 other balls . so like this u get a lot of extra cases .
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