Chapter 6 Section 7
Combinations and Permutations
Algebra 2 Notes – February 10, 2009
Warm-Ups: Candy Hearts Activity
WORK WITH A PARTNER

Step 1: Dump out your Candy Hearts. Count how many
total hearts you have.

Step 2: Count how many of each color you have.

Step 3: Find each probability


P(Purple) P (Orange or Green) P(Not White) P(Yellow)
Step 4: Eat candy and ENJOY!!! 
Factorials

Factorials:

Examples:

By Definition:
Permutations
 Permutation: an arrangement of items in a
particular order.
nPr : n items taken r at a time
n = total items
r = number of arrangements

Example: There are 4 brand new 16 year-olds waiting to
have their pictures taken for their driver’s license. How
many different ways can all four people be lined up?
More Permutations

Example: Seven golfers play in a tournament in
Hawaii. First, second, and third place awards will be
given out at the end of the tournament. How many
different ways can those awards be handed out?
n (total items) = ?
r (number of arrangements) = ?
nPr =
Permutations
 Permutation Formula:

Example: Imagine you’re cleaning your room. You
have 9 books needing to be put away. How many
different ways can you arrange those 9 books if there
is only room for 5 books on your bookshelf?
n=? r=?
Combinations

Combination: A selection of items in which order
doesn’t matter

Examples??? Can you think of anything?

You’re at Inta Juice and you decide to order a “Pickett Yourself”
smoothie. There are 6 different fruits to choose from but you
can only put 3 into your drink. How many different
combinations of fruit can go into your smoothie?
Identify n and r from the problem:
n = number of items to choose from
r = number of items being chosen
Combinations

Combination Formula:

Evaluate the following combinations:
C3
12
C5
10
C2
8
Combinations or Permutations??

Decide whether each of the following problems is
a combination problem or a permutation
problem. How do you know?

A reading course in world literature has 20 books on it. In how
many ways can you choose four books to read?

How many different nine-player batting orders can be chosen
from a baseball squad of 16?

You’re making a CD.You have chosen 10 of your favorite songs
but only have room for 4 more songs on the CD. How many
different ways can you chose those 4 songs?
Homework #21
 Pg
348 #1, 2, 10, 11, 21, 22, 29-32,
40, 56