Question

One mapping (function) is selected at random from all the mappings of the set \( A = \{1,2,3,\dots,n\} \) into itself. The probability that the mapping selected is one-one, is

• A. \( \frac{n!}{n^{n-1}} \)
• B. \( \frac{n!}{n^n} \)
• C. \( \frac{n!}{2n^n} \)
• D. None of the above

Hint:

Total functions from a set of size \( n \) to itself is \( n^n \), and bijections are \( n! \).

Answer 1

The Correct Option is B