A mapping is selected at random from the set | vedclass

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Question

(c)The total number of functions from $A$ to itself is ${n^n}$ and the total number of bijections from $A$ to itself is $n\,\,!.$

{Since $A$ is a f

Vedclass · Accepted Answer

$\frac{{(n - 1)\,!}}{{{n^{n - 1}}}}$

Vedclass · Answer

(c)The total number of functions from $A$ to itself is ${n^n}$ and the total number of bijections from $A$ to itself is $n\,\,!.$

{Since $A$ is a finite set, therefore every injective map from $A$ to itself is bijective also}.

$	herefore $ The required probability $ = \frac{{n\,\,!}}{{{n^n}}} = \frac{{(n - 1)\,\,!}}{{{n^{n - 1}}}}.$

A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is

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