Consider a collection of n individuals. Assume that each person's birthday is equall...

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 , denote the event that persons i and j have the same birthday. Show that these events are pairwise independent, but not independent. That is show that are independent, but the are not independent.