Permutations and Combinations
ES: Explicitly assess information and draw conclusion
Review: Counting Principle
1.) Carol has 4 skirts, 3 shirts, and 3 pairs of shoes. How many different outfits are possible?
2.) A bike
license plate consists of one letter followed by three numbers.
a.) How many license plates can be made if letters or numbers can repeat?
b.) How many license plates can be made if letters or numbers are not allowed to repeat?
3.) How many possible outcomes are there if you spin the spinner three times?
A
B
C
D
Review: Factorial
1.) 5!
2.) 3!
3.) There are 4 people in a line outside a movie theatre. how many different ways can
you arrange them?
Permutation Notation:
nPr
n = total number of items r = number choosing
PermutationAn arrangement in which order is important
(AB and BA are different)
Are the following permutations?
When lining 3 people up in line does the order matter?
How about just selecting 3 people, does order matter than?
When putting books on a shelf, does order matter?
When selecting three books to read, does order matter?
Examples:
1.) 6P2
2.) 8P3
3.) There are 5 contestants in the Mr. TEMS pageant. How many permutations are
possible if there is a 1st, 2nd and 3rd place winner?
4.) There are 50 numbers on a standard combination lock.
a.) How many 3-number arrangements are possible if
can repeat?
no number
b.) How many 3-number arrangements are possible if
numbers can repeat?
5.) There are 5 people in a group , only two can be lined up. How many ways can you
line them up?
Combination Notation
nCr
n = total number of items r = number choosing
CombinationsAn arrangement in which order does not matter.
(AB and BA are the same combination because the letters are the same and
the order does not matter)
Example : Selecting sandwich toppings
having lettuce and tomato on a sandwich is the same as having tomato and
lettuce
Formula:
nCr =
1.) 9C5
2.) 10C3
3.) From a group of 5 students, 3 students will be chosen for a school
technology committee. How many different combinations are possible?
4.) At the local pizza place, they have 9 different topping. You can order a pizza with
3 different toppings for $10. How many different types of pizza can be made?
5.) The DJ has 40 songs from the 80's. He needs to play exactly 5 songs at the
dance. How many 5 song combination can he make if the order he plays the
songs does not matter?
Demonstrate Understanding
1.) 10P4
2.) 7C3
3.) How many different 7 digit phone numbers are possible?
4.) Four Olympic gold medalist will pose together for a picture. How many ways
can they stand side by side in the photo?
Solve each using the counting principle, permutations or combinations.
5.) You have 9 book and want to display 5 on a shelf. How many different 5
arrangements are possible?
6.) You have 5 choices of sandwiches fillings. How many different sandwiches
could you make by choosing three of the five fillings?
7.) Mr. Cataldi selects a committee of 4 students from 25 students. How many
different committees could he make?
8.) Class officers are president, vice-president, secretary and treasurer. From a
class of 25 students, how many different groups of officers could students elect?
9.) There are 12 dogs in a Frisbee contest. How many ways can there be a winner and a
runner-up?