Consider a random collection of n individuals. In approximating the probability that no 3 of these individuals share the same birthday, a better Poisson approximation than that obtained in the text (at least for values of n between 80 and 90) is obtained by letting Ei be the event that there are at least 3 birthdays on day i, i = 1, . . . , 365.
(a) Find P(Ei).
(b) Give an approximation for the probability that no 3 individuals share the same birthday.