Please answer this question correctly. Show all steps and explain. Thank you.

l. A book club has 49 membersnone of which was born on a leap year. Assuming that each member is equally likely to be born on any of the 365 days of the year, independently of the other members, respond: (a) Let X be the random variable that counts the total number of combination of size 2 composed by members with a same birthday. What prevents X to have a Binomial ((2), 37:5) distribution? Explain! (b) What's the probability that X = 1? Explain! (c) Let Y be the random variable that counts the number of members born on July 4th. What's the probability that Y = 0? What's approximately this probability and theoretical upper-bound on the error? Explain your answers! ((1) Let Z be the random variable that counts the number of members born on a Monday. What's the distribution of Z? In theory, is this distribution well approximated by a Poisson distribu- tion? In the afrmative case, what's the rate of this Poisson? Explain your answers