Probability of selecting 4 balls of 4 different coulours from infite number of balls
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infinity
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Let us say that we have selected 'x1' blue balls, 'x2' red balls, 'x3' white balls and 'x4' grey coloured balls.
This means, x1+x2+x3+x4 = 12
Now, for an intance, 1+2+3+6 can be an answer. 0+0+0+12 can also be another answer
Hence, we need to find the non-negative integral solution for the equation
x1+x2+x3+x4 = n is
(n+k-1)C(k-1)
Here, n=12 and k=4
(12+4-1)C(4-1) = 15C3 = 455
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