question_answer

Let A and B be two finite sets having m and n elements respectively such that \[m\le n.\,\] A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is

A)            \[\frac{n\,!}{(n-m)\,!\,{{m}^{n}}}\]                                        

B)            \[\frac{n\,!}{(n-m)\,!\,{{n}^{m}}}\]

C)            \[\frac{m\,!}{(n-m)\,!\,{{n}^{m}}}\]                                       

D)            \[\frac{m\,!}{(n-m)\,!\,{{m}^{n}}}\]