A permutation <img alt="$(a_1,a_2,a_3,a_4,a_5)$" height="18" src="https://latex.artofproblemsolving.com/d/2/c/d2c536e5fd5bdfb01f8f1c33fd28404c8c91d589.png" width="130" /> of <img alt="$(1,2,3,4,5)$" height="18" src="https://latex.artofproblemsolving.com/b/5/f/b5fb4639b239e6737f5a8bf84413c28f5a67c065.png" width="90" /> is heavy-tailed if <img alt="$a_1 + a_2 < a_4 + a_5$" height="15" src="https://latex.artofproblemsolving.com/a/b/c/abc1273379f408ff91eea9658cad7102b8f6b189.png" width="139" />. What is the number of heavy-tailed permutations? <img alt="$\mathrm{(A)}\ 36\qquad\mathrm{(B)}\ 40\qquad\textbf{(C)}\ 44\qquad\mathrm{(D)}\ 48\qquad\mathrm{(E)}\ 52$" height="18" src="https://latex.artofproblemsolving.com/e/d/a/eda8cd5988ad27f79753ac51fb96080fa7c21c6c.png" width="388" />

Question No: 320

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

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

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Tags: Combinatorics

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