Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of $6$ hops, and end up back on the ground?
(For example, one sequence of hops is up-up-down-down-up-down.)
[2024-AMC8-q13.png](https://artofproblemsolving.com/wiki/index.php/File:2024-AMC8-q13.png)
$\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 12$
Looking at the answer choices, you see that you can list them out. 
Doing this gets you:
$UUDDUD$
$UDUDUD$
$UUUDDD$
$UDUUDD$
$UUDUDD$
Counting all the paths listed above gets you $\boxed{\textbf{(B)} \ 5}$.
~ALWAYSRIGHT11
~vockey(minor edits)