+544 Twelve points are given in the plane, so that no three points lie on the same line.
Five distinct segments joining pairs of these points are chosen at random, with all \binom{12}{2} = 66 such segments equally likely to be chosen. What is the probability that a pentagon is formed by the chosen segments? (The pentagon's five vertices must all come from the original set of 12 points.)
Explain your answer.
