Question

Let A be a set containing $10$ distinct elements, then the total number of distinct function from $A$ to $A$ is

• A. $10!$
• B. ${10}^{10}$
• C. $2^{10}$
• D. $2^{10}-1$

Answer 1

The correct option is B ${10}^{10}$

For a set containing $n$ elements, the total number of distinct functions form $A\times A$ will be $n^n$.
Here $n$ is $10$
Hence number of distinct functions, will be ${10}^{10}$.