Question: 2017 Fall Midterm - 3
Let $n \geq 1$ be an integer. Consider functions
$$
f : \{1,2,3,\dots,n\} \rightarrow \{1,2,3,\dots,7n\}
$$
such that, for each $i$ with $1 \leq i \leq n$, $f(i)$ is divisible by 7. How many such functions
are there?
(a)
$7^{n}$
(b)
$n^{n}$
(c)
$(7n)^{n}$
(d)
$n^{7n}$