A) \[\frac{1}{{{n}^{n}}}\]
B) \[\frac{1}{n\,!}\]
C) \[\frac{(n-1)\,!}{{{n}^{n-1}}}\]
D) \[\frac{n\,!}{{{n}^{n-1}}}\]
Correct Answer: C
Solution :
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}. \[\therefore \]The required probability \[=\frac{n\,\,!}{{{n}^{n}}}=\frac{(n-1)\,\,!}{{{n}^{n-1}}}.\]
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