Question

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

• A. $\frac{1}{n^n}$
• B. $\frac{1}{n!}$
• C. $\frac{(n-1)!}{n^{n-1}}$
• D. $\frac{n!}{n^{n-1}}$

Answer 1

The correct option is C $\frac{(n-1)!}{n^{n-1}}$

Total number of functions (mappings) from $A\to A=n^n$
Number of injective (one – one) functions
From $A\to A=n!$
$\therefore$ Probability =$\frac{n!}{n^n}=\frac{(n-1)!}{n^{n-1}}$