Math - Applied combinatorics

Assume G has 11 vertices. G and its complement G* together wil have C(11,2) = 55 edges. Since m <= 3n -6 in simple planar graphs, neither G nor G* can have more than 3(11) - 6 = 27 edges, or together more than 54 edges. Contradiction.

what is C(11,2) means?
how do u find 55 edges.......can u explain a little bit more please......i don't understand