Please show your work

Chapter 9

1. A mother, father, and their two children are to line up for a photo. In how many ways can these four family members line up so that the mother and father are next to each other? Be sure to show your work.

2. Given the set S = {A,B,C,D,E}, how many ways are there to

a. select two letters from S if repetition is allowed?

b. select two letters from S if repetition is not allowed?

c. select three letters from S if repetition is allowed?

d. select two letters from S such that the first letter is different from the second letter?

e. select three letters from S such that no two letters in the three selected letters are the same?

Chapter 10

1. If ten friends are born from 2000-2010, are at least two of the born in the same year?

___________________________________________________________________________________

2. Use the generalized definition of lexicographic order to order the following tuples according to lexicographic order.

(5,1,3,2), (4,5,6,1,2), (2,3,4), (7,2), (1,4,7), (5,2,1), (2,5, 3,4,7), (3), (4,2,1), (2,3), (1), (3,4,8)

Chapter 11

1. Consider the experiment of rolling one die one time.

a. List as a subset of the sample space the event E that the number of dots showing on the up face of the die is 6.

b. What is the probability that the number of dots showing on the up face of the die is 2 or 3?

___________________________________________________________________________________

Chapter 12

1. The following questions are based on the graph G pictured below.

5m k f h d a b C