The question says:in how many ways we could put 4 black,4 white,4 red balls in 6 different boxes?
boxes are distinguishable,black balls are identical,red balls are identical,and white balls are identical.
one or more box can remain empty.
i know number of ways to put k indistinguishable balls to n distinguishable boxes.but i don't know how to attack this problem because 3 different kind of balls.
Best Answer
Hint: Because colors are distinguishable, the answer is just how you put 4 red balls in 6 boxes times 4 white balls in 6 boxes, times 4 black balls in 6 boxes. Each color has the same number of balls, so they have the same number of combinations, so the answer is the number of ways to put 4 balls in 6 boxes, cubed (one time for each color, so three times multiplied)