Permutations and Combinations

Random Things to KnowDice (singular = “die”)Most cases: 6 sidedNumbers 1,2,3,4,5,6

Special Cases: 4 sided8 sided10 sided12 sided20 sided

Random Things to KnowCardsTypical Deck: 52 cards4 Suits (13 cards each)

Clubs Spades2-10 2-103 Face 3 Face1 Ace 1 Ace

Hearts Diamonds2-10 2-103 Face 3 Face1 Ace 1 Ace

Random Things to Know

Counting Principle

If you have 6 shirts and 3 pants how many different outfits can you create?

Counting Principle

If you have_________________and you have _______________,

Then there are ways of doing both

M = N = Number of outfits you can make = So the total is

Counting Principle

When flipping a coin 15 times how many results are possible?

*Think how many different results are there when you flip a coin*

_________________

Counting Principle

A restaurant has on its menu• 5 choices for appetizers• 3 choices for main course• 2 choices for dessert

How many different meals (appetizer, main course, and dessert) can you choose?

_____________________

FactorialsMany equations in probability use ____________. A ____________ is a mathematical concept that is represented by an _____.

Ex1:

Ex2:

To do a factorial in the calculator: ________________________________

Let’s Practice……

• A student is to roll a die and flip a coin. How many possible outcomes will there be?

Answer: _________• For a college interview, Robert has to choose what to wear

from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from?

Answer:__________

Permutations

You and your 3 friends are standing in line to buy tickets to a movie. How many ways are

there for you to arrange yourselves?

PermutationsRemember the Counting Principle:

M*N = total number of ways to select items

• How many choices do you have for the first spot? ___

• How many choices do you have for the second spot?__• How many choices do you have for the third spot?___

• How many choices do you have for the fourth spot?__• So________________________

PermutationsDef:_________________________________________________________________

In races who comes in 1st, 2nd, and 3rd is very important for prizes, and rankings. The order

does matter.

Permutations

Permutations• You can use your calculator to find

permutations• To find the number of permutations of 10 items

taken 6 at a time (10P6): • Type the total number of items• Go to the MATH menu and arrow over to PRB• Choose option 2: nPr• Type the number of items you want to order

Let’s Practice……

• Find the number of ways to arrange the letters ABC.

Answer:_______

• A combination lock will open when the right choice of three numbers (from 1 to 30, inclusive) is selected. How many different lock combinations are possible assuming no number is repeated?

Answer:_______

CombinationsIf you have 5 trophies but only space on a shelf for

2 of them how many different ways can you arrange your trophies?

BIG QUESTION: DOES ORDER MATTER??

CombinationsRemember the Counting Principle:

M*N = total number of ways to select items

How many trophies can you choose between?______

How many spots are there?______

So…

Combinations

Def:_______________________________________________________________________

If you order pizza it doesn’t matter if you tell them “Peperoni, Pineapple, and Sausage” or

“Sausage, Peperoni, and Pineapple” NO! It all goes on the pizza!

___________________________

Combinations

n = total number of elementsr = number of items chosen

Combinations• You can use your calculator to find combinations• To find the number of combinations of 10 items taken 6 at a

time (10C6): • Type the total number of items• Go to the MATH menu and arrow over to PRB• Choose option 3: nCr• Type the number of items you want to order

Let’s Practice……

• To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible?

Answer:_______

• A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting line up of one center, two forwards, and two guards?

Answer:_______