1. ## exponential generating function

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

2. Originally Posted by sw2010
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.

3. so would the answer to (b) be f^(7-n)

4. Originally Posted by sw2010
so would the answer to (b) be f^(7-n)
No, you need a new "f"-- this time the EGF for the number of ways to arrange the objects if each object appears no more than 7 times.