2010 AMC8 Problem 25

#1
Everyday at school, Jo climbs a flight of \(6\) stairs. Jo can take the stairs \(1\), \(2\), or \(3\) at a time. For example, Jo could climb \(3\), then \(1\), then \(2\). In how many ways can Jo climb the stairs?

\( \textbf{(A)}\ 13 \qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24 \)