How many ways can you distribute 10 candies among 5 kids, if each kid must get at least one candy?
Distribute one candy to each kids first.
5 candies are left, and I can distribute to them in any configuration.
I have 55 = 3125 ways to do so.
Oh, yes. Considering only the cases that satisfy the condition is quite troublesome, so I want to make sure that each kid gets one candy at the very beginning, so there will be less constraints to consider.