Q139 / 200 · Manipal (MET) 2014 · Mathematics
One mapping (function) is selected at random from all the mappings of the set $A=\{1,2,3, \ldots, n\}$ into itself. The probability that the mapping selected is one-one, is
- A$\frac{n!}{n^{n-1}}$
- Correct answerB$\frac{n!}{n^n}$
- C$\frac{n!}{2 n^n}$
- DNone of the above
Solution
Total number of mappings from a set $A$ having elements into itself is $n^n$.
And the total number of one to one mapping is $n!$ $\therefore$ Required probability $=\frac{n!}{n^n}$
And the total number of one to one mapping is $n!$ $\therefore$ Required probability $=\frac{n!}{n^n}$
Hence, the correct answer is option: 'B'.