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Heavy-Tailed Permutations

Source: AMC 12 2008A #21

February 17, 2008
AMC

Problem Statement

A permutation (a1,a2,a3,a4,a5) (a_1,a_2,a_3,a_4,a_5) of (1,2,3,4,5) (1,2,3,4,5) is heavy-tailed if a_1 \plus{} a_2 < a_4 \plus{} a_5. What is the number of heavy-tailed permutations? <spanclass=′latex−bold′>(A)</span> 36<spanclass=′latex−bold′>(B)</span> 40<spanclass=′latex−bold′>(C)</span> 44<spanclass=′latex−bold′>(D)</span> 48<spanclass=′latex−bold′>(E)</span> 52 <span class='latex-bold'>(A)</span>\ 36 \qquad <span class='latex-bold'>(B)</span>\ 40 \qquad <span class='latex-bold'>(C)</span>\ 44 \qquad <span class='latex-bold'>(D)</span>\ 48 \qquad <span class='latex-bold'>(E)</span>\ 52
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