Question

The number of one-one functions that can be defined from $A=\{4,8,12,16\}$ to $B$ is $5040,$ then $n\left(B\right)=$

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

The correct option is D $10$

The first element $4$ of $A$ can be mapped to any of the $n$ elements in $B$
Similarly second element $8$ of $A$ can be mapped to any of $(n-1)$ elements in $B$
$\Rightarrow$ Total no of one - one functions is
$n(n-1)(n-2)(n-3)=5040$
$\Rightarrow n=10$