What is the formula to find number of one one function ?

Solution :

If A and B are two sets having m and n elements respectively such that m $\le$ n, then the total number of one-one functions from A to B is

$^nC_m \times m!$

where m! is m factorial.

For example, Let set A have 3 elements and set B have 4 elements, then number of one-one functions are $^4C_3 \times 3!$ = $4 \times 6$ = 24