AMC 12 2008a 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?

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