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 \(a_0=7\).