Question

Find number of distributions for 5 red balls,5 white balls and 5 blue balls in 3 different boxes

Answer 1

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Answer 2

Answer:

Assuming balls of the same color are identical.

Number of ways we can distribute 5 red balls in 3 different boxes

= (5+3-1)C(3-1) = 7C2 = 21

(reference: formula 5 )

Similarly,

Number of ways we can distribute 5 white balls in 3 different boxes = 21

Number of ways we can distribute 5 blue balls in 3 different boxes = 21

Therefore, required number of ways

= 21×21×21 = 9261