9. Consider a collection of n individuals. Assume that each person's birthday is equally likely to be any of the 365 days of the year and also that the birthdays are independent. Let A_ij denote the event that persons i and j have the same birthday, i ≠ j. Show that these events are pairwise independent.

That is, A_ij and A_rs are independent but the (ⁿ₂) events A_ij i ≠ j are not independent.