N-gon

How many diagonals has convex 11-gon?

Result

x =  44

Solution:

n=11 C2(11)=(112)=11!2!(112)!=111021=55  x=(n2)n=5511=44n = 11 \ \\ C_{{ 2}}(11) = \dbinom{ 11}{ 2} = \dfrac{ 11! }{ 2!(11-2)!} = \dfrac{ 11 \cdot 10 } { 2 \cdot 1 } = 55 \ \\ \ \\ x = { { n } \choose 2 } - n = 55 - 11 = 44



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