1. How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable but the boxes are not?
2. How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable and the boxes are distinguishable?
3. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?
4. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?
5. How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?
6. 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?
