Discrete Mathematics Mid Term Review Questions Chapter 8

8.1

5

How many ways are there to pay a bill of 17 pesos using the currency described in Exercise 4, where the order in which coins and bills are paid matters?

6

Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. That is, sequences a_1, a_2,...,a_k, where a_1 = 1, a_k = n, and a_j < a_j+1 for j = 1, 2,...,k − 1.

b) What are the initial conditions?

c) How many sequences of the type described in (a) are there when n is an integer with n ≥ 2?

8-23

26

29

31

33-45

8.2

17,26,31,35,39,44,48,49

8.4

23,28,31,

35-41

44

8.5

14,15,25

8.6

15,

17,18,19

22,23,24