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?

tomtom Nov 3, 2023

#1**-1 **

Each of the 4 balls has 8 choices for the box it goes into.

ANSWER: 8^4 = 2^12 = 4096

GaSucksBigDix Nov 4, 2023