Combinatorics

Business Week: Closets- Google images

So, you’ve proven to some people the value of math. Now it’s time to tackle a large problem and go national with math.





The problem you intend to tackle is the amount of clothes bought and thrown out. People think that there is only one combination for each outfit. They think that you need completely different articles of clothing to have a different outfit



The problem you intend to tackle is the amount of clothes bought and thrown out. People think that there is only one combination for each outfit. They think that you need completely different articles of clothing to have a different outfit

However, you intend to show them that with just 4 outfits they can have many, many different outfits.


You intend to go national with this by sharing your knowledge about combinatorics with a famous artist who will spread the word.


Luckily, you come across an artist by the name of WonderfullyExcelent. He is perfect for what you want to do. He is worried about the enviroment and the affect that all these clothes will have on it.

You intend to go national with this by sharing your knowledge about combinatorics with a famous artist who will spread the word.


You tell WonderfullyExcelent to choose 4 pants, 4 shirts, 4 pairs of shoes, 4 belts and 4 sweaters, a total of 20 articles of clothing.


Now, you ask him how many outfits do you think you can make with this? He says 4. You say over 500.




He doesn’t believe you and tells you to prove it.





So you do.



There are two ways to do this, you explain. You can label every outfit 1,2,3 or 4 and then see how many ways you can mix and match them. It would look like this:

Belt 1 Shoe 1 Shirt 1 Glasses 1 Pants 1



Combination 1Combination 2

Combination 3




So you do.


However, this would take way too long so an easier way would be to use the “choose formula”. Which is:



nCr

Where n is the number of objects to choose from, and r is the number of objects to be arranged.



nCr


So....

4C1 4C1 4C1 4C1 4C1

Belts Shoes Shirts Glasses Pants



nCr


So....

4C1 4C1 4C1 4C1 4C1

Belts Shoes Shirts Glasses Pants

They are all 4C1 because you have 4 of each and only 1 place to arrange each one. Shoes on you feet, glasses on you face, pants on your legs, belt on your hips and shirt on your chest.


Now it’s time for the grunt work!



4C1 equals 4 so our little chart now looks like this:




4 4 4 4 4 Belts Shoes Shirts Glasses Pants




4 4 4 4 4 Belts Shoes Shirts Glasses Pants

We now multiply all of this together because that will tell you the amount of ways you can arrange all of these articles of clothing together.

4 * 4 * 4 * 4 * 4 = 1024

This is the amount of outfits you can make out of just 20 articles of clothing!

WOW

!Congratulations!

WonderfullyExcelent is amazed and you’re already receiving national attention for you work with math!

Combinatorics

Education

closets google images

combinatorics business

different outfit business

c 1equals4so

n c r wherenis

different articles of

number of objects

value of math