This is a classic problem referred to as the birthday problem
The probability that at least two people share a birthday is 1 minus the probability that no one shares a birthday.
Choose the first person. He can have any birthday. Now choose a second person. The probability that the second person doesn't' share the same birthday as the first person is 364/365 (excluding a birthday on Feb 29). Now choose a third person. The probability that the third person doesn't share the same birthday as the first or second person is 363/365. And so on.
P(none of the 22 people share a birthday) =
so P(at least two of the 22 people share a birthday) =