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
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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