Random ideas to solve Alex's Anniversary Paradox



I've been thinking a bunch about how to tackle this problem. It seems like my trip to the barber shop seems like a weird variant of the Birthday Paradox: What is the probability, in a group of n randomly chosen people, at least three will have the same name and wedding day?

I've poked around stats exchange and found some general solutions to the birthday paradox, including an R implementation. Though, I'm not convinced that this is a good approach. How do you maintain assumptions and also account for names?

It seems like a better way would be to collect data on birthdays and wedding anniversaries, and calculate the distribution. A project for another day...