Three diagonals of a regular 11-sided regular polygon are chosen ; probability of parallelism

Hint: Let $L$ be the number of lines (which you can compute easily). As each line is parallel to a unique side of the $11$-gon, they are partitioned into$~11$ classes of size $L/11$ according to their direction. To count how many among the $\binom L3$ triples contain at least one parallel pair, you can subtract from $\binom L3$ the number of choices that avoid any parallel pairs. The number is obtained by multiplying the number $\binom{11}3$ of choices of $3$ distinct directions by the number $(L/11)^3$ of choices of one line from each direction class.

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