Counting

Division problem

There are 2 patterns.

Pattern 1= Division of distinguishable items.

How many ways are there to divide 5 distinguishable balls into 3 boxes?

Answer will be further divided based on the following 3 conditions.

Boxes are distinguishable or indistinguishable?
Box can get multiple balls or can get only one ball?
Box can be empty or must have at least one ball?

Pattern 2= Division of indistinguishable items.

How many ways are there to divide 5 indistinguishable balls into 3 boxes?

Answer will be further divided based on the following 3 conditions.

Boxes are distinguishable or indistinguishable?
Box can get multiple balls or can get only one ball?
Box can be empty or must have at least one ball?