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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?

 Nov 3, 2023
 #1
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Each of the 4 balls has 8 choices for the box it goes into.

ANSWER: 8^4 = 2^12 = 4096

 Nov 4, 2023

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