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Discrete Structures – CNS2300

Discrete Structures – CNS2300. Text Discrete Mathematics and Its Applications (5 th Edition) Kenneth H. Rosen Chapter 4 Counting. Section 4.3. Permutations and Combinations. Picture Taking Time. Picture Taking Time. Permutations. Arrangements Order is important I P Y I Y P

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Discrete Structures – CNS2300

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  1. Discrete Structures – CNS2300 Text Discrete Mathematics and Its Applications (5th Edition) Kenneth H. Rosen Chapter 4 Counting

  2. Section 4.3 Permutations and Combinations

  3. Picture Taking Time

  4. Picture Taking Time

  5. Permutations • Arrangements • Order is important IPY IYP Same elements, different order (permutation)

  6. How Many Permutations (Arrangements)? IYP This can be solved using the product rule. IPY YIP YPI PIY PYI There are three decisions to be made. For the first decision, three choices For the second decision, two choices For the third decision, one choice Therefore (3)(2)(1)=6 permutations

  7. zvfzvrzfvzfrzrvzrfvfzvfrvrfvrzvzrvzf fvzfvrfrzfrvfzv fzrrvfrvzrfvrfzrzfrzv Have 4, arrange 3 zvfr

  8. Permutations The number of r-permutations of a set with n distinct elements is

  9. Form a Committee of Three

  10. Good Choice

  11. Another Choice, Same Committee First Choice

  12. Combinations • Subsets • Order is not important IPY IYP Since order is not important, these are the same subset (combination)

  13. How Many Combinations (Subsets)? If there are three objects and you are choosing three, there is only one subset, since order is not important. IYP IPY YIP YPI PIY PYI

  14. zvfzvrzfvzfrzrvzrfvfzvfrvrfvrzvzrvzf fvzfvrfrzfrvfzv fzrrvfrvzrfvrfzrzfrzv Have 4, choose 3 zvfr

  15. zvfzvrzfrzrvzrfvfrvrfvrzvzr fvrfrzfrvfzrrvfrvzrfvrfzrzfrzv Have 4, choose 3 zvfr

  16. zvfzvrzfrzrvzrfvfrvrfvrzvzr fvrfrzfrvfzrrvfrvzrfvrfzrzfrzv Have 4, choose 3 zvfr

  17. zvfzvrzfrzrfvfrvrf fvrfrzfrvfzrrvfrfvrfzrzf Have 4, choose 3 zvfr

  18. zvfzvrzfrvfrvrffvrfrv rvfrfv Have 4, choose 3 zvfr

  19. zvfzvrzfrvfr Have 4, choose 3 zvfr If you start with a set containing four objects, there are only four subsets that contain 3 objects.

  20. Combinations The number of r-combinations of a set with n elements, where n is a positive integer and r is an integer with equals

  21. So, you see. Counting is very simple.

  22. Corollary

  23. Alternate Notation

  24. Calvin and Hobbes - Watterson You know, I don’t think Math is a Science. I think it’s a religion. A religion?

  25. Calvin and Hobbes - Watterson Yeah. All these equations are like miracles. You take two numbers and when you add them, they magically become one new number! No one can say how it happens. You either believe it or you don’t

  26. Calvin and Hobbes - Watterson This whole book is full of things that have to be accepted on faith! Its a religion

  27. Calvin and Hobbes - Watterson And in the public schools no less. Call a lawyer. As a math atheist, I should be excused from this.

  28. finished

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