Question

Find the number of all one-one functions from set $A=\{1,2,3\}$ to itself.

Answer 1

Since $f$ is one-one, thus every element of $\{1,2,3\}$ has either of image $\{1,2,3\}$ an that image is unique.
Therefore,

Total no. of one-one functions $=3!=3\times 2\times 1=6$