Surjections from $5$ to $3$

#surjections#IE#count

Statement

Count surjections from a $5$ -element set to a $3$ -element set.

Hint

IE: $3^5-3\cdot2^5+3\cdot1^5$ .

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Compute. $243-96+3=150$ .

Alternative. $3!\,S(5,3)=6\cdot25=150$ .

Conclusion. $150$ surjections.