Probability of matching birthdays (2–5 out of N people, displayed as a graph)

This graph illustrates the probability of matching birthdays. It is well known that the probability is highest when two out of N people share a birthday, but
as the number increases—to three, four, and so on—the probability drops sharply.
The calculation formula uses the approximation formula also employed by the R functions `pbirthday` and `qbirthday`:
Diaconis, P. and Mosteller, F. “Methods for studying coincidences.” J. American Statistical Association.
This formula is used here.