Permutations refer to arrangements where order matters. There are many real-life applications of permutations including combination locks, car races, license plate numbers, seating arrangements, and creating passwords. Permutations are used to calculate the number of possible combinations when order is important, such as the order of finishing cars, arrangement of letters in a password, or how objects like books or trophies can be arranged on a shelf.

1. PERMUTATION
REAL LIFE APPLICATION OF PERMUTATION

2. Definition:
 Permutation of a set of objects is an arrangement of those objects into a
particular order. For example, there are six permutations of the set{1, 2,
3}, namely set(1, 2, 3),(3, 1, 2),(2,1,3), (1,3,2),(2,3,1) and (3,2,1).
OR
 All the possible arrangements of a collection of things, where the
order is important.
 It is important to know that a permutation refers to an arrangement where
order matters.
 It is not only the thing that we face in our competitive exams. We face this
in our day to day life.

3. PRACTICAL APPLICATION OF PERMUTATION

4. Digital lock
 A “combination lock” should really be called a
“Permutation lock”. Permutation lock has
three inputs. If the order of input changes,
it won’t unlock. Though the number are same,
but order plays its role.

5. Car Race
 For example, there are 8 cars in a race and the goal
was to predict the correct finishing order of all 8 cars.
This is a permutation problem because order matters.
How many different ways can the cars finish in the race?
The answer is
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 40320.
The probability of picking the correct order
would be very small indeed.

6. Car Number Plate
 Another excellent example is the number plate people have
on their cars. This is a unique for each person because no two
cars are allowed to have the same
number plate.

7. Choosing Clothes
You have 3 shirts and 2 paints . Using these shirts and
paints you want to create maximum number of pairs of
shirt and a paint.
How many way you can pair the
shirts and paints.
If there are 15 shirts and 10 shirts you can
make 150 pairs of shirt and paint.

8. Waiting Room
 There are three candidates for an interview. There are three
post to be filled
* Manager * Supervisor * Specialist
In this case, order of picking an employee plays important
role.
If the order change their roles will also change.
*Manager * Supervisor * Specialist
*Supervisor * Specialist * Manager
*Specialist * Manager *Supervisor

9. Telephone Dilemma
Nearly everyone has a phone number, so this is
a very good real world example. 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 remember is that it use the
number 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.

10. Seating Dilemma
 Seating Dilemma one of the most key components in 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 crowed rather than 600,000,000,
if who sat where wasn’t a trivial matter? If a
person use a permutation they don’t have to
play this pointless, agitating guessing game and
can plan accordingly.

11. Seating Arrangement
Seating arrangement is important to a teacher because this can
be a way to manage behavior in class. For example, He may
choose to not let two noisy student sit together or hew can put
three students sit side by side so they can help each other.
Seating arrangements of executive in board meetings may be
important especially if ranks the person are holding in a
company is considered.

12. Trophy Line up
Everybody loves showing off their
achievements and what better way to display
your magnificence than through your seemingly
endless amount of trophies? A display way is
quite effective, but there are so many ways
to display the trophies, and you 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 permutation.

13. Making password
 Making password is essential in making sure our information
online is safe and protected. It is important to always change
passwords regularly to prevent hacking and fraud. The
number of password can be made is determined by
permutation.

14. Making Words
 English letters are 26 only. Out of these 26 letters. We formed
lacs and lacs of word by using these 26 letters which was done
by arranging these 26 letters in various permutation and
combination.

15. PAINTING
You want to paint your room. Your room
has 4 walls and you have 3 paint colors.
Each wall can be painted 3 different colors
but you have 4 sides. You can paint it in
4*3*2*1=24 different ways.

16. Book Arrangement
 An example of permutations would be the arrangement of
books on a shelf .An easy one is to say there are five
different book… how many ways can you arrange them on
shelf?
Then you have five choices for the first
book four choices for the second book
three choices for the third book...
5*4*3*2*1=120 ways to set books on a shelf.

17. Jobs where a person can use permutation

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

19. Combo Lock Designer
These people design the locks that are used for gates 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.

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