Find the exponential generating function for a_n, the number of different arrangements of n objects chosen from 5 different types of objects with each object appearing
a) at least 3 times
b) no more than 7 times
Hint for a):
Suppose you just have only 1 type of object. Then no matter how many of the objects you have, there is only 1 way to arrange them. What is the EGF of the number of ways to arrange the objects if each object appears at least 3 times? Call this EGF f. Then the answer to a) is just f^5.