HOMEWORK RULES
Lots of confusion 
 Submit via email by noon on
Saturday
 Please learn how to use a scanner
and scan your homework in. I need
procedures not only the answers.
 Thank you!

LAST LECTURE

Basic Counting Principle

Arithmetic Sequences

Geometric Sequences

Shifted Sequences
2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049
PERMUTATION
WB Math Group
TOOLS


Trees
Simple Algebra
ROCK PAPER SCISSORS
Player2
Player1
Rock
Rock
Paper
Scissors
Rock
Paper
Paper
Scissors
Rock
Scissors
Paper
Scissors
ROCK PAPER SCISSORS LIZARD SPOCK
ROCK PAPER SCISSORS LIZARD SPOCK
ROCK PAPER SCISSOR ON STEROIDS
1.3 trillion
permutation
A SIMPLE PROBLEM


You have three shirts and four pairs of pants.
How many outfits consisting of one shirt and one
pair of pants can you make?
Shirts – S1, S2, S3, Pants – P1, P2, P3, P4
S1
P1
P2
S2
P3
P4
3
P1
P2
4
S3
P3
P4
12
P1
P2
P3
P4
ANOTHER SIMPLE PROBLEM

How many three letter words can be formed by
letters in DOG?
D
O
G
O
G
G
O
D
G
G
D
D
O
O
D
3
2
1
6
MULTIPLICATION PRINCIPAL

- number of ways A and B can occur

- number of ways A can occur

- number of ways B can occur
Event A
Event B
1
1
2 …
2
1
2 …
…
…
1
2 …
SOME SIMPLE PROBLEMS
In how many ways can we arrange four different
books on a shelf?
 Your math club has 20 members. In how many
ways can it select a president, a vice-president
and a treasurer if no member can hold more than
one office?
 Previous problem without the limitation of no
member can hold more than one office?
 In how many ways can we arrange n different
books, where n is a positive integer?

A LITTLE ALGEBRA

Factorial:

Compute the following:




9!/8!
42!/40!
8! – 7! (hint: law of distribution)
For each of 8 colors, you have one shirt and one
tie of that color. How many shirt-and-tie outfits
can you make if you refuse to wear a shirt and a
tie of the same color? Can you express your
answer in terms of factorials?
A SLIGHTLY HARDER PROBLEM

A club has n members, where n is a positive
integer. We want to choose r different officers of
the club, where r < n, such that no member can
hold more than one office.
In how many ways can we fill the first office?
 Once we’ve filled the first office, in how many ways
can we fill the second office?
 If we proceed as in the previous two steps, in how
many ways can we fill the
office?
 In how many ways can we choose the r officers?

PERMUTATION

The number of permutations of size r from a
group of n objects is
BRAIN EXERCISE

Compute the following





P(8, 3)
P(20, 4)
P(30, 1)
P(6,5)
P(50, 3)
What is P(n, n) for any positive integer n? does it
make sense?
 What is 0!
 Simplify

SOME EXERCISES




You have 5 shirts, 6 pairs of pants and hats, how
many outfits can you make consisting of one shirt,
one pair of pants and one hat?
How many 3-letter combinations can be formed if the
second letter must be a vowel (a,e,i,o,u) and the third
letter must be different from the first letter?
In how many ways can you order 7 different colored
hats in a row?
Our basketball team has 12 members, each of whom
can play any position. In how many ways can we
choose a starting lineup consisting of a center, a
power forward, a shooting forward, a point guard, and
a shooting guard?
SOME HARDER PROBLEMS






How many permutations does GAUSS have?
How may different license plates can be made where
each plate has three distinct lower case English
letters?
How many integers between 100 and 999 inclusive
consist of distinct odd digits?
How many integers between 100 and 999 have
distinct digits?
There are 10 points where no three points are on one
line. How many straight lines can be made by
connecting two points?
10 boys and 9 girls sit in a row of 19 seats. How many
ways can this be done if
All boys sit next to each other and all girls sit next to each
other
 Each child has only neighbors of the opposite gender?


10 boys and 9 girls sit in a row of 19 seats. How
many ways can this be done if

Each child has only neighbors of the opposite gender?