Question 238028
Out of 10 people you have 45 possible pairings of different people in each pair.
This would be a combination and the formula would be n! / (x!*(n-1)!)


With each one of these pairings, the probability that the two persons involved do NOT have the same birthday would be 364 / 365 if we ignore february 29th.


The probability that all of these pairing would NOT have the same birthday is therefore (364/365)^45 = .883859763


This means that there's at least a 12% chance that one of them will have the same birthday.


If I include February 29th, then the total possible birthdays becomes 366.


The probability of not being both on the same day is then 365/366 which changes the results a little but not much.


Numbers become (365/366)^45 = .88415836


we're still talking about 12% chance of at least one of the pairs being born on the same day.


I don't know if I calculated the february 29th probability correctly, but even if not, the difference would still be negligible.


That's what I think.


I checked the logic with smaller numbers and it appears to be sound.