Question

Let $A$ be a set containing $10$distinct elements. Then the total number of distinct functions from $A$ to $A$, is?

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

Answer 1

The correct option is B

${10}^{10}$

Explanation for correct answer:

Finding the total number of distinct functions:

Let $A$ be a set containing $10$distinct elements $\left\{a_1,a_2,...,a_{10}\right\}$

Finding the distinct function from $A$ to $A$.

Functions from $A$ to$A$, $f\left(a_m\right)=a_n$, where $m$ and $n$ranges from $1$ to $10$

For $m=1$ it has $10$possibilities. likewise $m$ ranges from $1$ to $10$.

Therefore, the total number of distinct functions=$10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10\times 10$

The total number of distinct functions from $A$ to $A$, is ${10}^{10}$

Hence, option (B) is the correct answer.