Solutions  Homework #1
Chapter 1
Problems
1. Problem 5
: For years, telephone area codes in the United States and Canada consisted of a sequence
of three digits. The first digit was an integer between 2 and 9; the second digit was either 0 or 1; the
third digit was any integer between 1 and 9. How many area codes were possible? How many area
codes starting with a 4 were possible?
Using the Multiplication Rule for Counting
, there are:
8
·
2
·
9 =
144 possible area codes
.
If the
area code must start with a 4, there are: 1
·
2
·
9 =
18 possible
.
2. Problem 8c
: How many different letter arrangements can be made from the letters MISSISSIPPI?
If the 11 letters in “MISSISSIPPI” can be distinguished from each other, there are 11!
orderings
of these letters.
However, since there are 4!
ways to arrange the “I”’s, 4!
ways to arrange the “S”’s, and 2!
ways
to arrange the “P”’s for any given permutation so that the same word appears, then there are:
11!
4!4!2!
=
34650
different letter arrangements from “MISSISSIPPI.”
3. Problem 10
: In how many ways can 8 people be seated in a row if:
(a) there are no restrictions on the seating arrangement.
There are 8! =
40320
total permutations of 8 people in a row.
(b) persons A and B must sit next to each other.
There are: 7 ways to choose 2 adjacent seats for persons A and B,
2 ways to choose which seat A gets & which seat B gets, &
6! ways to seat the remaining 6 people.
=
⇒
7
·
2
·
6! =
10080
total ways.
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 Spring '08
 SMITH
 Mississippi, ways, possible outcomes

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