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Question

There are unlimited number of Red, White, Blue and Green balls. The balls are all the same except the color of each ball. What are the number of ways in which selection of 10 balls can be made?

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Solution

Here, we need maximum 10 Red balls, 10 White balls, 10 Blue balls and 10 Green balls to have all selections of 10 balls.

Now, we need integral solution of

Red + White + Blue + Green = 10.

We know that the Integral solution of x1+x2+...+xr=n is given by n+r1Cr1

Here n=10, r=4

Number of ways of selections are 10+41C41

= 13C3

= 13×12×113×2×1

= 13×2×11

= 286

286 ways of selection of 10 balls can be made.



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