A couple of days ago I logged into Facebook to see that 4 of my friends all had a birthday that day. Being the nerd that I am, I immediately tried to figure out the probability of this occurrence out of my total of 493 friends. I have run through a couple of scenarios, (binomial and 493 simultaneous independent events) both of which have much smaller probabilities than I would have thought. I also tried applying the birthday paradox logic, but just confused myself, so I thought I would throw it out there for some summer fun. Might I pick your brain for how I would find the probability that exactly four of my 493 Facebook friends would have a birthday on the same day?