Question

Set $A$ has $3$ elements and set $B$ has $4$ 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)

$24$

To define the injective functions from set $A$ to set $B$, we can map the first element of set $A$ to any of the $4$ elements of set $B$.
Then the second element can not be mapped to the same element of set $A$, hence, there are $3$ choices in set $B$ for the second element of set $A$.
Similarly there are $2$ choices in set $B$ for the third element of set $A$.
Hence the total number of injective functions are $4\times 3\times 2=24$