Developing Expert Voices 2009

1. Combinatorics Business Week: Closets- Google images

2. 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. 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. Business Week: Closets- Google images

3. 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 Business Week: Closets- Google images

4. 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 However, you intend to show them that with just 4 outfits they can have many, many different outfits. Business Week: Closets- Google images

5. You intend to go national with this by sharing your knowledge about combinatorics with a famous artist who will spread the word. Business Week: Closets- Google images

6. 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. Business Week: Closets- Google images

7. 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. Business Week: Closets- Google images

8. Now, you ask him how many outfits do you think you can make with this? He says 4. You say over 500. 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. Business Week: Closets- Google images

9. 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. 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. Business Week: Closets- Google images

10. 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. 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. Business Week: Closets- Google images

11. 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: Now, you ask him how many outfits do you think you can make with this? He says 4. You say over 500. 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. He doesn’t believe you and tells you to prove it. So you do. Business Week: Closets- Google images Belt 1 Shoe 1 Shirt 1 Glasses 1 Pants 1 Belt 1 Shoe 1 Shirt 1 Glasses 1 Pants 2 Belt 1 Shoe 1 Shirt 1 Glasses 2 Pants 2 Combination 1 Combination 2 Combination 3

12. However, this would take way too long so an easier way would be to use the “choose formula”. Which is: Business Week: Closets- Google images

13. However, this would take way too long so an easier way would be to use the “choose formula”. Which is: n C r Where n is the number of objects to choose from, and r is the number of objects to be arranged. Business Week: Closets- Google images

14. However, this would take way too long so an easier way would be to use the “choose formula”. Which is: n C r Where n is the number of objects to choose from, and r is the number of objects to be arranged. So.... 4 C 1 4 C 1 4 C 1 4 C 1 4 C 1 Belts Shoes Shirts Glasses Pants Business Week: Closets- Google images

15. However, this would take way too long so an easier way would be to use the “choose formula”. Which is: n C r Where n is the number of objects to choose from, and r is the number of objects to be arranged. So.... 4 C 1 4 C 1 4 C 1 4 C 1 4 C 1 Belts Shoes Shirts Glasses Pants They are all 4 C 1 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. Business Week: Closets- Google images

16. Now it’s time for the grunt work! Business Week: Closets- Google images

17. Now it’s time for the grunt work! 4 C 1 equals 4 so our little chart now looks like this: Business Week: Closets- Google images

18. Now it’s time for the grunt work! 4 C 1 equals 4 so our little chart now looks like this: 4 4 4 4 4 Belts Shoes Shirts Glasses Pants Business Week: Closets- Google images

19. Now it’s time for the grunt work! 4 C 1 equals 4 so our little chart now looks like this: 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! Business Week: Closets- Google images

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