Question

Let A and B be two finite sets having m and n elements respectively. If m $\le$ n, the total number of injective functions from A to B is

• A. $m^n$
• B. $n^m$
• C. $\frac{n!}{(n-m)!}$
• D. $n!$

Answer 1

The correct option is C $\frac{n!}{(n-m)!}$

Since, m $\le$ n, injective functions from A to B are defined and the total of such functions is
${}^n{P}_m=\frac{n!}{(n-m)!}$