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Permutations 123465764393 090879607679.pptx
- 1. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like. EXAMPLE
- 2. ALGEBRA
- 3. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 4. PERMUTATION
- 5. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 7. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 8. CIRCULAR
- 9. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 10. FACTORIAL
- 11. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 12. ARRANGE
- 13. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like.
- 14. OBJECT
- 15. WARM-UP ACTIVITY Mechanics: The puzzles can be a combination of pictures, homonym or what the pictures sounds like. -
- 16. STATISTIC
- 17. Learning Objectives At the end of the lesson, the students will be able to: • illustrate the permutation of objects; and • solve problems involving permutations.
- 18. PERMUTATIONS
- 19. Permutation A permutation is an arrangement of things in definite order or the ordered arrangement of distinguishable objects without allowing repititions among the objects. In general, if n is a positive integer, then n factorial denoted by n! is the product of all integers less than or equal to n. n! = n·(n－1)·(n－2)·…·2·1 As special case, we define 0! = 1
- 20. Examples Compute: a) 7! b) 𝟖! 𝟔! c) 4!5! Solutions: a) 7! = 7·6·5·4·3·2·1 = 5,040 b) 8! 6! = 8·7·6! 6! = 56 c) 4!5! = (4·3·2·1)(5·4·3·2·1) = 2,880
- 21. nPr - We can now obtain the formula in computing the number of permutations of n things taken n at a time, or taken r at a time. A. The number of permutations of n things taken n at a time is given by: nPn = n! the number of permutations of n taken r at a time.
- 22. Examples Compute: a) 7P7 b) 5P5 c) 4P4 Solutions: a) 7P7 = 7! = 7·6·5·4·3·2·1 = 5,040 b)5P5 = 5! = 5·4·3·2·1 = 120 c) 4P4 = 4! = 4·3·2·1 = 24
- 23. nPr - B. The number of permutations of n things taken r at a time is given by: nPr = 𝒏! (𝒏−𝒓)! where r < n the number of permutations of n taken r at a time.