4. Suppose that the number of cars visiting New Paltz has Poisson distribution with a parameter A> 0. There are three types of cars-diesel, sedan, and truck. The probability of randomly chosen car is a diesel, sedan, or truck is P1, P2, and p3 with p + p2 + P3 = 1 and the event of each car being a certain type is independent of each other. Let X, Y, Z be numbers of diesel cars, sedans, or trucks during one day. (a) Suppose that there are n distinct items. We want to divide n items into three groups, group A, B, and C with a, b and c elements with a+b+c= n. Show that the number of different grouping is (a,b,c)= = n! alxb!xcl (b) Show that (a+b+c)! abc. P1P2P3 X a+b+c (a+b+c)! ex