# Homework #9

Due in lecture, Thursday May 16. Please do the homework in a workbook.

# From the Text

Complete the following questions from the text:

• Section 7.2: 12, 30
• Question 12 hint: $$r=-1,1,2$$.
• Section 7.5: 6, 20
• Question 6: “pairwise disjoint” means that the intersection of any two of the sets is empty.
• Section 7.6: 16, 18, 24
• Question 16: your answer can contain a $$D_k$$ indicating a number of derangements. No need to simplify/expand it.
• Question 24 hint: Use a combinatorial argument. Let $$k$$ be the number of elements that stay fixed in a permutation. How many ways were there to choose them? How many ways can the remaining $$n-k$$ elements be placed?
• Section 8.1: 4, 8, 24

# Questions

1. Use generating functions to solve the recurrence $$a_n=4a_{n-1}+6$$ with $$a_0=7$$.