2008 AMC 12A Problem 21

A permutation (a_1,a_2,a_3,a_4,a_5) of (1,2,3,4,5) is \textit{heavy-tailed} if a_1 + a_2 < a_4 + a_5. What is the number of heavy-tailed permutations?

\mathrm{(A)}\ 36\qquad\mathrm{(B)}\ 40\qquad\textbf{(C)}\ 44\qquad\mathrm{(D)}\ 48\qquad\mathrm{(E)}\ 52

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.