How many functions (Counting problem) Let $A$ be a set of size $25$ and let $B$ be a set of size $17$. How many functions $f\colon A\to B$ are there?


$17!$
$\frac{25!}{17!}$
$17^{25}$
$25^{17}$


I think the answer is 3. Is it?
A set is a group of unique elements (in opposed to a multi-set).

A function $f : A \rightarrow B$ maps every element in the domain $A$ to a single element in the range $B$.

You have $25$ elements in the domain $A$ and $17$ elements in the range $B$.

Each element in the domain $A$ must be mapped to an element in the range $B$:


The 1st element in the domain $A$ has $17$ mapping options in the range $B$
The 2nd element in the domain $A$ has $17$ mapping options in the range $B$
The 3rd element in the domain $A$ has $17$ mapping options in the range $B$
...
The 25th element in the domain $A$ has $17$ mapping options in the range $B$


So the total number of different mappings (i.e., functions) from $A$ to $B$ is: $$17 \times 17 \times 17 \times \dots \times 17 = 17^{25}$$
Yes: (cardinality of codomain) to the power of (cardinality of domain) is right.