How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

1.How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?

2.How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

3.How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?

4.How many ways are there to put 6 balls in 3 boxes if three balls are indistinguishably white, three are indistinguishably black, and the boxes are distinguishable?

5.I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(5a) The candies are all different and the lunch boxes are all different?

(5b) The candies are all the same and the lunch boxes are all the same?

(5c) The candies are all the same and the lunch boxes are all different?

(5d) The candies are all different and the lunch boxes are all the same?

(5e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

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