Cool combinatorics.....

Let \((a_1,a_2,a_3,\ldots,a_{12})\) be a permutation of \((1,2,3,\ldots,12)\) for which

\(a_1>a_2>a_3>a_4>a_5>a_6 \mathrm{\ and \ } a_6<a_7<a_8<a_9<a_{10}<a_{11}<a_{12}.\)

How many such permutations are there?


An example of such a permutation is

\((6,5,4,3,2,1,7,8,9,10,11,12)\) .

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