2013 Pascal Problem 23

Joshua chooses five distinct numbers. In how many different ways can he assign these numbers to the variables p, q, r, s, and t so that p < s, q < s, r < t, and s < t?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 8\quad \textbf{(E)}\ 15

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.