Question

Set $A$ has $n$ elements. The number of functions that can be defined from $A$ into $A$ is:

• A. $n^2$
• B. $n!$
• C. $n^n$
• D. $n$

Answer 1

Answer: (C)

$n^n$

The number of functions that can be defined from a set into another set can be found by ${\text{(Number of elements in co-domain)}}^{\text{Number of elements in domain}}$

Since, set $A$ has $n$ elements, we have

Number of elements in co-domain $=$ Number of elements in domain $=n\left(A\right)=n$.

Therefore, number of functions that can be defined from $A$ into $A$ $=n(A{)}^{n\left(A\right)}=n^n$.