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In how many ways can $4$ balls be placed in $3$ boxes if the balls and boxes are both distinguishable, and no box can be empty?

In how many ways can $4$ balls be placed in $3$ boxes if neither the balls nor the boxes are distinguishable, and no box can be empty?

In how many ways can $4$ balls be placed in $3$ boxes if the balls are indistinguishable, and the boxes are distinguishable, and no box can be empty?

In how many ways can $4$ balls be placed in $3$ boxes if the balls are distinguishable, and the boxes are indistinguishable, and no box can be empty?

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