Surjections from $4$ to $3$

#surjections#IE#count

Statement

Count surjections from a $4$ -element set to a $3$ -element set.

Hint

IE: $3^4-3\cdot2^4+3\cdot1^4$ .

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Compute. $81-48+3=36$ .

Alternative. $3!\,S(4,3)=6\cdot6=36$ .

Conclusion. $36$ surjections.