Let there be n balls and m urns.

1). If all balls are distinct and all urns are also distinct then number of ways in which the balls can be put in the urns is $\displaystyle m^n$

2). If balls are all alike but urns are distinct then the number of ways are $\displaystyle \binom{n+m-1}{n}$

3). If balls are distinct but urns are not then????

4) If both are alike then????

what is the solution to the last two?