Three diagonals of a regular 11-sided regular polygon are chosen ; probability of parallelism Could someone help me with this?
Suppose P is an 11-sided regular polygon and S is the set of all lines that contain two distinct vertices of P. If three lines are randomly chosen from S, what is the probability that the chosen lines contain a pair of parallel lines ?

But you are choosing three lines.  The probability that you have calculated is for choosing a pair of parallel lines.  The question asked is you randomly choose 3 lines and that it contain exactly one parallel pair.  I would agree with Steven that the probability space is 55C3.  Each edge will have 4 parallel lines and only that.  The lines made up of other vertices are not parallel to any other.  
Thus, the answer that I think is
11C1*5C2*50C1/55C3 = 100/477.  The rational is 11C1  is the choice that you make of 11 sets of 5 parallel lines (including the edge).  You choose 2 of these 5 and hence 5C2 and the other line you choose among 50 lines that are not parallel to the chosen pair.
Let me know if my reasoning is correct, Mark.
Thanks
Satish
