chance discovery of parallel family

My daughter at university asked me (October 2014) to check some details about the post-graduate course she is on. A related Google search took me straight to a student society relating uniquely to that course, and I noticed that a member of the student committee (ie someone else currently on the course) had the same surname, which is not common. I looked up her details using free online birth-marriage-death indexes and found that she was born in the same medium-sized town as my daughter, some 100 miles away from the university. It turned out, that like my daughter, she is one of four sisters, who likewise were all born in this same town, and whose births were registered in exactly the same four years. We are definitely not related, do not have any particular shared (cultural, religious etc) background that would lead us to have large families and to the best of my knowledge we have never met or come across each other in any way. There are other strong parallels between the two sets of four sisters and on further research there are clear parallels between the two families over several generations, relating to key names, places and family size. However, the direct parallels of surname, birth place, family relationships and registration year for the two sets of sisters seem most relevant as these are facts are visible in the official records and indeed are essentially the only facts visible there. </p> <p>I made a rough calculation of the probabilities of all this and they seem very remote. </p> <p>There are 80 people in total on this post-graduate course at any time, essentially all British. Approximately 1 in 2100 births in England & Wales every year is registered with our (English) surname. Approximately 1 in 100 of these births (ie 4 or 5 a year) is in the town where all 8 girls were born. I do not know the frequency of there being four full sisters in a family, I guessed the rough probability of someone having three full siblings was at least 1 in 10, and then 1 in 8 for them being all girls. I do not have the maths to work out the rough probability of the four girls from each family being registered in the same years, though some cross over was likely as one from each family is a student at the same time on the same post-graduate course, albeit some students on the course are in their 40s. For various reasons I guessed this possibility at 1 in 48 but this may be conservative. </p> <p>Therefore, the overall possibility of this set of coincidences, ie the chances of my daughter finding in a given year that there is another girl on her course with the same surname, born in the same town, with three sisters also born there, and a total correspondence between their registered birth dates seems to me to be VERY roughly (2100/80) x 2 x 100 x 10 x 8 x 48 = 1 in 20,160,000. Is this broadly correct? Is the coincidence extraordinary or exaggerated in some important way?<br />