let (a1, a2, a3, . . . , a12) be a permutation of (1, 2, 3, . . . , 12) for which a1 > a2 > a3 > a4 > a5 > a6 and a6 < a7 < a8 < a9 < a10 < a11 < a12. 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.
