Permutations%20and%20Combinations

1
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Biancas family needs to choose exterior paint
for their new house. The wall colors are white,
green, and beige. The trim colors are white,
green, blue, and cocoa. How many combinations of
wall color and trim are possible?
12
12-6
2
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
(For help, go to Lesson 12-4.)
Use the Counting Principle to find the number of
outcomes. 1. Roll 2 number cubes. 2. Choose
three different letters. 3. Select a month and
a day of the week. 4. Toss a coin 4 times.
Check Skills Youll Need
12-6
3
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Solutions 1. first number second
number 6 outcomes 6 outcomes 6 ? 6 36
2. first letter second letter third
letter (different from 1st) (different from
1st 2nd) 26 choices 25 choices 24
choices 26 ? 25 ? 24
15,600
12-6
4
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Solutions (continued) 3. month day 12
choices 7 choices 12 ? 7 84
4. first toss second toss third toss fourth
toss 2 outcomes 2 outcomes 2 outcomes 2
outcomes 2 ? 2 ? 2 ? 2
16
12-6
5
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Find the number of permutations possible for the
letters H, O, M, E, and S.
There are 120 permutations of the letters H, O,
M, E, and S.
Quick Check
12-6
6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
In how many ways can you line up 3 students
chosen from 7 students for a photograph?
7 6 5 210 Simplify
You can line up 3 students from 7 in 210 ways.
Quick Check
12-6
7
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
In how many ways can you choose two states from
the table when you write reports about the areas
of states?
Make an organized list of all the combinations.
12-6
8
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
(continued)
AL, CO AL, ME AL, OR AL, TX Use
abbreviations of each CO, ME CO, OR CO,
TX states name. First, list all ME, OR ME,
TX pairs containing Alabama. OR, TX Continue
until every pair of states is listed.
There are ten ways to choose two states from a
list of five.
Quick Check
12-6
9
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
How many different pizzas can you make if you
can choose exactly 5 toppings from 9 that are
available?
You can make 126 different pizzas.
Quick Check
12-6
10
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Tell which type of arrangementpermutations or
combinationseach problem involves. Explain.
a.  How many different groups of three vegetables
could you choose from six different
vegetables? b.  In how many different orders
can you play 4 DVDs?
Combinations the order of the vegetables
selected does not matter.
Permutations the order in which you play the
DVDs matters.
Quick Check
12-6
11
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Find the number of permutations or
combinations. 1. Find the number of permutations
of the last four digits in the phone number
5551234. 2. In how many ways can you
arrange six out of eight books on a shelf?
3. In how many ways can you choose three
different items from a menu containing seven
items? Does each problem involve permutations
or combinations? 4. How many different groups of
four ice cream toppings can you choose from
sixteen toppings? 5. In how many different
ways can five students line up?
24
20,610
35
combinations
permutations
12-6