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

    $\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}$

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