# Placing different color balls into distinguishable boxes [closed]

In how many ways can you place 4 red balls, 5 blue balls, and 6 yellow balls in 4 distinguishable boxes? (Balls with same color are indistinguishable)

## closed as off-topic by José Carlos Santos, TheSimpliFire, Arnaud Mortier, Empty, uniquesolutionFeb 8 '18 at 12:26

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HINT: If you had only the $4$ red balls, this would be a standard stars-and-bars problem; the same is true if you had only the $5$ blue balls or only the $6$ yellow balls. Solve each of these three problems separately, and combine the solutions appropriately. Note that the three problems really are independent of one another.

$$(^{4+4-1}C_{4-1}) \times (^{5+4-1}C_{4-1})\times(^{6+4-1}C_{4-1})=(^{7}C_{3}) \times (^{8}C_{3})\times(^{9}C_{3})$$