arrangements how many ways can i arrange the following candles?

Arrangements

How many ways can I arrange the following candles?

Fundamental Counting PrincipleHow many different combinations of can be

made with 4 types of ice cream and 3 toppings?

M & M’s

Peanuts

Sprinkles

Fundamental Counting PrincipleFundamental Counting Principle - when one event or outcome can happen in a certain number of ways and a second event can happen in a certain number of ways, you can multiply to find how many ways the two events can happen together.

M & M’s

PeanutsSprinkles

(4 types of ice cream) x (3 types of topping) = 12 different combinations

Permutations

How many ways can I arrange the following candles?

PermutationsPermutation - the number of ways in which a set of items can be arranged. (The order does matter.)

To find permutations, there are 3 methods:1. Make an organized list of the different

arrangements (this was done in the example)

2. Multiply the number of objects being arranged by each counting number less than it. (this is called a factorial)

3. Use the formula

Permutations1.Multiply the number of objects being arranged by

each counting number less than it. (this is called a factorial)

2. Use the formula

There were 3 candles, so we will perform 3!

3 x 2 x 1 = 6

So, there are 6 different arrangements of these candles.

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P ( 0! Is equal to 1 )

Permutations1.Multiply the number of objects being arranged by

each counting number less than it. (this is called a factorial)

2. Use the formula

There were 3 candles, so we will perform 3!

3 x 2 x 1 = 6

So, there are 6 different arrangements of these candles.

)!(

!),(

rn

nrnP

)!33(

!3)3,3(

P ( 0! Is equal to 1 )

CombinationsCombinations - choosing a subset from a group of objects. (The order of the subset does not matter.)

To find the # of Combinations, there are two methods:

1. Make an organized list.

2. Use a formula.

Example: How many different way can I arrange 5 students, when the order does matter? (Susan, Kristi, Brad, Jamie, Mark)

1. Make an organized list.

Susan

Kristi

Brad

Jamie

Mark

CombinationsExample: How many groups of 3 students can be chosen from a class of 5 students, when the order doesn’t matter? (Susan, Kristi, Brad, Jamie, Mark)

1. Make an organized list.

2. Use a formula.

Susan

Kristi

Brad

Jamie

Mark

= _____________ = ______________ = _____________ =

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