Let \((a_1,a_2,a_3,\ldots,a_{12})\) be a permutation of \((1,2,3,\ldots,12)\) for which \(a_1>a_2>a_3>a_4>a_5>a_6 \mathrm{\ and \ } a_6< a_7< a_8< a_9< a_{10}< a_{11}< a_{12}.\) 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.

(第二十四届AIME2 2006 第4题)