**Permutations in the REAL WORLD!!**

by: Victoria E, Tyler G, and Sam W

by: Victoria E, Tyler G, and Sam W

Everyday Situations where Permutations are quite useful- Example 1: Seating Dilemmas

Everyday Situations where Permutations are quite useful- Example 2: Trophy line up

Everybody loves showing off their achievements(at least those who are confident anyway), and what better way to display your magnificence than through your seemingly endless amount of trophies? A display case is quite effective, but there are so many ways to display the trophies, and you(being the picky individual you are) would prefer to group trophies of the same achievements together. To figure out how many ways you can display the same ones together within the number of trophy slots allotted, you can use a permutation.

Solution

Problem#2: Names for the Plate

**Conclusion**

Refresher: What are Permutations?

Definition: All possible arrangements of a collection of things, where the order is important.

Overview: Permutations are essentially just an expression that determines the number of all possible orders of events, people, or objects if the order of occurrence is of importance. The formula for a permutation is

Problem #1: Telephone Dilemma

Telephone Dilemma: Solution

In all these examples, the main goal is to determine how many possible combinations are available, but with the condition that order is of importance is still kept in mind. Meeting the order constraint is the most critical part since some situations are tailored on the foundation that the order matters and nothing else.

Jobs where a person could use Permutations

IANA: The IANA(Internet Assigned Numbers Authority) are responsible for assigning the IP addresses for all the technology in the world that interacts with the internet. They use permutations to pick an address that is functional, open, and meets the requirements for a specific type of device

Combo Lock designers: These people design the locks that are used for gates, bikes, and lockers. They use permutations to assign combos that haven't been used previously, are the only combination that opens a lock, and cannot be cracked.

Seating is one of the most key components in any event. The combinations are endless and can be extremely frustrating - or so it seems. Wouldn't it be a lot simpler if you knew there are only 6 ways to seat a crowd rather than 600,000,000, if who sat where wasn't a trivial matter? If a person uses permutations they don't have to play this pointless, agitating guessing game and can plan accordingly.

The Goal of these Examples

How Permutations are useful

Well, as previously stated the situations are direct embodiments of what a permutation is. However, a person will truly benefit from knowing if they are skilled at it in an in depth level. They'll be able to decipher what needs a permutation and what needs a combination, solve these situations at a faster speed compared to other methods, and use the answers to adequately analyze the conclusion of their situation.

While doubtful that this topic could actually benefit us and be used outside of class,our misconception has been denounced and we are now aware of the many uses for permutations and as a team, and we hope you do too.

Ace, a hopeless romantic, is having a teenage life crisis. He received a girl's number, but dropped the piece of paper into a chimney and it was incinerated to beautiful ashes by accident. All he remembers is that it used the numbers 0-9 and consisted of 7 numbers. Help Ace figure out if asking the girl for her number is worth it by figuring out how many possible combinations of numbers are possible .

There are nine possible numbers to choose from so that's are N

There are 7 number slots to fill so that is our R

The Facts

The Math/ Computation

N!

(n-r)!

9!

9!

(9-7)!

2!

9!

1. Plug your variables

in and simplify

2.Multiply the

factorials out

and divide.

2!

362,880

2

=

181,440

There are 181,440 possible combinations or telephone numbers.(Sorry Ace. Maybe Next Time

Jane has recently graduated college and her parents, being the wonderful people they are, have decided to give her a car. When she goes to register her car she is told that she has to pick out 6 letters for her license plate. Jane, wanting to keep her swag in tact, only wants to use letters from the words STARBUCKS and YOLO and does not want to use the same letter twice. How many license plate options are available for Jane to choose from?

SECRET HIDDEN CHALLENGE PROBLEMS

Betcha weren't expecting this, huh?

1: How many 6-letter-long-combinations can be made from the word supercalifragilisticexpialidociou-s without using any vowels or repeating any letters? (NOTE: Does NOT need to be real words. CAN BE GIBBERISH.)

2: There are half-as-many kids as there is days in February on a non-leap year trying out for twice-as-many-days-in-a-week- that-end-in-day spots on a sports team. How many ways can the spots be filled?

In order to solve this problem you have to figure how many letters are there in the words that aren't duplicates. There are eleven from both words that aren't duplicates.

n!

(N-R)!

11!

(11-6)!

11!

5!

1) Plug in

variables

and simplify

11!

5!

39,916,800

120

332,640

2)Multiply

your factorials

an divide

There 332,640 combinations available for Jane to choose from