Problem 7

$12$ children are playing with $6$ skipping ropes. Each child grabs one end of a rope, and then they all line up forming two parallel lines, in such a way that no two children holding two ends of the same rope are in the same line. The children then pull the skipping ropes taut, and count how many pairs of ropes there are crossing each other. If the children arranged themselves randomly, what is the probability that the number of crossing pairs of ropes is exactly $9$? Give your answer rounded to $3$ decimal places.