Question

A mapping is selected at random from a set $A=\{1,2,...,10\}$ into itself. The probability that the mapping selected is an injective is

• A. $\frac{10}{{10}^9}$
• B. $\frac{9!}{{10}^9}$
• C. $\frac{9}{10!}$
• D. none of these

Answer 1

The correct option is B $\frac{9!}{{10}^9}$

Let $n\left(A\right)$ represent the number of elements of set $A.$

$n\left(A\right)=10$

Number of function mapping from $A$ to $A=$ ${10}^{10}$

Out of these, the number of injective functions are $10!$

Thus $p\left(A\right)=\frac{10!}{{10}^{10}}=\frac{9!}{{10}^9}$