1. Fundamental Counting Principal
Algebra Name:___________________________________
Permutations and Combinations Date:_______________________Block:________
Fundamental Counting Principal
Scenario 1: You are buying a Honda. You can either get an Accord or a Civic. Your options for color are red, black, or silver. Your options for the interior color are black, gray, and tan. How many options do you have?
Scenario 2: How many lunches can you create? You have three entree choices: chicken, fish, and pasta. You have two side dish choices: green beans or french fries.
Scenario 3: You are ordering a case for your iPod. You can choose from 30 colors for the main shell, 32 colors for the protective band, and 200 decals for the cover. How many different
cases are possible?
Scenario 4: Passwords - You are creating an password that is NOT case sensitive. The password must be 6 characters in length and can contain either numbers or letters. How many passwords are possible?
How would the problem change if the password WAS case sensitive?
Scenario 5: License Plates-Pennsylvania License Plates consist of 3 letters followed by 4 numbers. How many license plates are available?
Scenario 6: Phone Numbers- How many 7-digit phone numbers are available for each area code? (NOTE: 7-digit phone numbers cannot begin with a 0 or 1).

2. Permutations
An ordering of a set of objects is called a ____________________________________.
This mathematical operation is called ____________.
The symbol for factorial is ___.
n! is defined as the product of n with all subsequent positive integers less than n.
Note: 0! = 1
Permutation
Notation: P(n, r) or nPr
n is the number of objects you are choosing from
r is the number of objects you are putting in order
P(5, 2)
12P7
8P8
P(4, 8)
P(5, 2)
12P7
Enter n
Math
PRB
#2) nPr
Enter r
8P8
P(4, 8)
Example 1: Ten people are competing in a race. How many ways can first, second, and third prize be awarded?
Example 2: How many ways can you arrange 5 out of 7 DVDs?
Example 3: How many ways can we select a president, vice president, and secretary from this class?
Example 4: Students are completing project presentations. How many orders of 5 students out of 20 can be created?

3. n! C(n,r)= nCr = (n-r)!r! Combinations
A COMBINATION is a selection of objects where the order of the objects does NOT matter. The number of combinations of n objects taken r at a time is: n!
(n-r)!r!
C(n,r)= nCr =
Example 1: Six students from a group of nine are chosen to represent their school at a conference. How many ways can the six students be chosen?
Example 2: You have ____ songs on your iPod. How many ways can you select 3 songs to listen to?
Example 3: How many different 5-card hands are possible from a standard deck of 52 cards?
Permutations vs. Combinations
You have a total of 12 books on the floor.
How many ways can you select 5 books and arrange them on a shelf?
How many ways can you select 5 books?
There are 18 students in this class.
How many ways can you select a committee of 3 students?
How many ways can you select a president, vice president, and secretary?
Example 1: At a musical festival there are 12 bands that are performing. How many different possibilities are there of seeing 4 bands?
Example 2: A contestant on a game show has 5 boxes to choose from for a prize. How many ways can he choose 2 prizes?

4. Algebra 2 Name: _________________________
Practice Worksheet Date: _________________________
Directions: Determine whether each problem is a permutation or combination. Write the calculator notation for the problem, then solve.
1. Twenty singers are trying out for the spring musical. In how many different ways can the director choose a duet?
2. Twenty singers are trying out for the spring musical. In how many ways can the director choose a lead and an understudy?
3. A box contains 20 marbles. How many ways can 5 marbles be chosen?
4. Aaron can afford to buy two of the six DVDs that he wants. How many possible pairs could he buy?
5. You have 12 books. Your bookshelf will hold nine books. How many ways could you select nine books for the shelf?
6. You still have 12 books. Your smaller bookshelf will hold 5 books. How many ways could you select and arrange 5 novels on the smaller bookshelf?
7. Eight toppings are available for a pizza. In how many ways can Rose choose three toppings?
8. How many committees of five students can be selected from thirty students?
9. How many panels with a president, vice president, secretary, treasurer, and historian can be chosen from thirty students?
This last problem is neither a permutation nor a combination. Show work for how to solve it.
10. Lauren has 6 new shirts, 4 new pair of pants, and 2 new belts. How many outfits can she create provided she must choose exactly one of each?