find the coefficient of x^6 in (1+ x)^12

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In this expansion we know that there are 13 terms which mirror each other starting with x and ending with 1. We know that the 6th power is in the exact middle of the expansion and thus will be the largest coefficent.  Here is the expanded version

x^12+ 12x^11+ 66x^10+ 220x^9+ 495x^8+ 792x^7+ 924x^6+ 792x^5+ 495x^4+ 220x^3+ 66x^2+ 12x+ 1

As you can see, the 6th power term is the greatest coefficent and the other terms mirror one another moving away in both directions.
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