2006 AIME II Problem 4

Let \left(a_{1}, a_{2}, a_{3}, \ldots, a_{12}\right) be a permutation of
(1,2,3, \ldots, 12) for which $$ a_{1}>a_{2}>a_{3}>a_{4}>a_{5}>a_{6} \quad \text { and } \quad a_{6}<a_{7}<a_{8}<a_{9}<a_{10}<a_{11}<a_{12}
$$ An example of such a permutation is (6,5,4,3,2,1,7,8,9,10,11,12).
Find the number of such permutations.