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Topology

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Number of Maps

TOPO-WEKHEF

Let:

$A=\{1,2,3,4,5\}$
$B=\{1,2,3\}$
$C=\{1,2,3,4\}$

How many maps from $A$ to $C$ can be written as compositions of surjections from $A$ to $B$ and injective maps from $B$ to $C$?

A

$600$

B

$200$

C

$972$

D

$23328$

E

None of the above.