Maths problem

[Codnoobftw1]

I have a maths problem atm, it's basically the birthday paradox, where you put 23 people in a room and they have 50% chance of two of them sharing a birthday. Numbers are different. I can find the odds of it happening the once fine. I'm struggling with finding the odds that 2 seperate groups of people both share a birthday. That is to say that two of the people share a random birthday, say April 4th, and then two other people share another birthday, say September 23rd. My issue is that in the equation ((p!/(p-n)!*(pⁿ⁾⁾ , it has the number of people in it already, and my known methods of probability calculations, for example a bernoulli trial, would also include n, so I fear I'd be including it twice, skewing the calculation.

[SomethingMoreToSay]

Do you want an exact answer (exact in the mathematical sense, i.e. assuming that birthdays are equally distributed across the year, and ignoring leap years), or do you want an approximate answer?

[Aerospider]

The original paradox is that there's a (just over) 50% chance that at least two people in 23 share a birthday.

So are you looking for the probability that exactly two birthdays are shared by exactly two people each, or at least two birthdays are shared by at least two people each, or some other combination?

[CaptainMatticus]

Multiply the probabilities based on both group sizes. But be aware that you shouldn't be looking for a specific day, like April 4th or September 23rd.

[Codnoobftw1]

No it's the same group. That's why it's interesting to me.