Question

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

• A. ${10}^{10}$
• B. $101$
• C. $2^{10}$
• D. $2^{10-1}$

Answer 1

The correct option is A

${10}^{10}$

Explanation for the correct option:

Find the total number of distinct function:

Domain : $A:\left\{1,2,3,4,\dots ..10\right\}$

Co domain : $B:\left\{1,2,3,4,\dots ..10\right\}$

$\therefore$Total number of distinct functions $=10\times 10\times 10\dots ..10$ times

$={\mathbf{10}}^{\mathbf{10}}$

Hence, Option ‘A’ is Correct.