Question

Set $A$ has three elements and set $B$ has four elements. The number of injections that can be defined from $A$ to $B$ is

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

Answer 1

Answer: (C)

Since $3<4$, injective functions from $A$ to $B$ are defined and the total number of such functions is
${}^4{P}_3=\frac{4!}{\left(4-3\right)!}=4\times 3\times 2\times 1$
$=24$.