Combinations and Permutations Notes
Combinations and permutations determine the number of ways to choose a certain
number of items from a given group of items.
"My fruit salad is a combination of apples, grapes and bananas"
"The combination to the safe was 472"
Identify each example as a combination or permutation.

3 people are picked from a group of 10.

Determine the numbers of ways 6 people finish in race if there are no ties and
everyone finishes the race.

Choosing 3 ice cream toppings from 5 in the ice cream shop.

Determine the number of unique license plates made from 4 digits and 3 letters.

Three players from the chess club of 10 members are chosen to go to the
tournament.
The factorial function (symbol: !) just means to multiply a series
of descending natural numbers. Examples:



4! = 4 × 3 × 2 × 1 = 24 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040 1! = 1 Note: it is generally agreed that 0! = 1. It may seem funny that multiplying no numbers together gets you 1, but it helps simplify a lot of equations. On your graphing calculator: Put the number in first then hit: MATHPRB#4
Find: 3!
10!
0!
Permutation Formula
where n is the number of things to choose
from, and you choose r of them
(No repetition, order matters)
Example:
How many different ways can a chairperson and an assistant chairperson
be selected for a research project if there are seven scientists available?
Combination Formula
where n is the number of things to choose
from, and you choose r of them
(No repetition, order doesn't matter)
Example:
Given the letters A, B, C, D in how many ways can you choose 2 letters?
1.
Practice
Art, Becky, Carl, Denise, and Ed all want to go to the concert. However,
there are only 3 tickets. How many ways can they choose the 3 who get to
go to the concert?
Combination or Permutation?
2.
A combination lock has 36 numbers on it. How many different 3-number
combinations are possible if no number may be repeated?
Combination or Permutation?
3.
Solve it.
Solve it.
Arrange the following in order from smallest to largest:
24C6
24P6
24!
Combinations and Permutations Worksheet
1.
Name_______________________
How many permutations of 3 different digits are there, chosen from the ten
digits 0 to 9 inclusive?
2.
Elections are being held for student representatives, and next year’s freshman
class will determine which two students will be chosen. If five students are
running for election, how many different groups of two can be elected to
represent the freshman class?
Combination or Permutation?
3.
The new computer desk for your room has enough shelf space to have three
reference books. Your parents purchased a set of four reference books for you.
How many different ways can you place three of the reference books on the shelf
of your new desk?
Combination or Permutation?
4.
Solve it.
Your favorite pizza parlor only offers five toppings and your budget for the
party will allow you to purchase pizzas with only three toppings. If no pizza can
have one topping twice, how many three-topping pizzas do you and your
friends have to choose from?
Combination or Permutation?
5.
Solve it.
Solve it.
A coach must choose five starters from a team of 12 players. How many
different ways can the coach choose the starters?
Combination or Permutation?
Solve it.
6.
The local Family Restaurant has a daily breakfast special in which the customer
may choose one item from each of the following groups:
Breakfast Sandwich Accompaniments
Juice egg and ham
egg and bacon
egg and cheese breakfast potatoes
apple slices
fresh fruit cup
pastry orange
cranberry
tomato
apple
grape a.) How many different breakfast specials are possible?
b.) How many different breakfast specials without meat are possible?
7.
There are fourteen juniors and twenty-three seniors in the Service Club. The club
is to send four representatives to the State Conference.
How many different ways are there to select a group of four students to attend
the conference?
Combination or Permutation?
Solve it.
8.
a.)
9.
Which of the following is NOT equivalent to
b.)
c.)
d.)
In how many ways can 3 vases be arranged on a tray?
Combination or Permutation?
10.
?
Solve it.
For a study group, 4 people are chosen at random from a group of 10 people.
How many ways can this be done?
Combination or Permutation?
Solve it.