# 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