Distributions

In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?

 

In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?

 

In how many ways can $4$ balls be placed in $8$ boxes if the balls are indistinguishable, and the boxes are distinguishable?

 

In how many ways can $4$ balls be placed in $8$ boxes if the balls are distinguishable, and the boxes are indistinguishable?