Question

Set $A$ has $3$ elements and set $B$ has $4$ elements.The number of surjections that can be defined from $A$ to $B$ is

• A. $144$
• B. $12$
• C. $24$
• D. $64$

Answer 1

Answer: (C)

$24$

Set A has $3$ elements and set $B$ has $4$ elements.
First element in set $A$ can be mapped to any of the $4$ elements in set $B$ in $4$ ways.
Second element in set $A$ can be mapped to any of the $3$ remaining elements in set $B$ in $3$ ways.
Third element in set $A$ can be mapped to any of the $2$ remaining elements in set $B$ in $2$ ways.
No of surjections $=4\times 3\times 2=24$
Hence, option C.