Answer to Question #23286 in Statistics and Probability for Georg Koester

Question

What is the probability of obtaining 6 pairs in the following circumstance? A pair is defined as both numbers in a pair being the same (n1=n2) within a possible number range of 0-1000. Each pair is found within a different set of 4 random numbers in that range, of which there are 17 sets? Secondly, what is the probability that two of those pairs have the same pairs of numbers (n1x=n2x=n1y=n2y)? Please state and explain your calculations in a way that a layperson can understand.