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

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