Question

The number of injections that are possible from $A$ to itself is $720,$ then $n\left(A\right)=$

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

Answer: (B)

$6$

first element of $A$ in domain can be mapped to
any of the $n$ elements of $A$ in range.
$2^{nd}$ element of $A$ in domain can be mapped to any of $(n-1)$ elements of $A$ in range.
$\therefore$ Total no of injections possible is
$n\times (n-1)\times (n-2)...\times 3\times 2\times 1=n!$
$\therefore n!=720$
$\Rightarrow n=6$