Permutation of Distinct Objects.pdf
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This document discusses four counting techniques: systematic listing, tree diagrams, the fundamental counting principle (FCP), and permutations. It provides examples of using each technique to solve problems involving counting possible outcomes. FCP states that if there are m ways to do one thing and n ways to do another, there are m*n ways of doing both. Permutations use factorials to count arrangements of distinct objects where order matters. The document gives examples of using permutations to count arrangements of people in roles and letters in words.
Permutation of Distinct Objects.pdf
- 1. four counting techniques prepared: ms. rigen v. maalam
- 2. review
- 3. systematic listing COUNTING TECHNIQUES making a table fundamental counting principle tree diagram
- 4. Tree diagram It uses line segments originating from an event to an outcome FCP It states that "when there are m ways to do one thing, and n ways to do another, then there are (m)(n) ways of doing both."
- 5. Sarah goes to her local pizza parlor and orders a pizza. She can choose either a large or a medium pizza, can choose one of seven different toppings, and can have three different choices of crust. How many different pizzas could Sarah order? previous quiz
- 6. Sarah goes to her local pizza parlor and orders a pizza. She can choose either a large or a medium pizza, can choose one of seven different toppings, and can have three different choices of crust. How many different pizzas could Sarah order? previous quiz
- 7. Pizza: 2 sizes, 7 toppings, 3 crusts By FCP: (2)(7)(3) = 42 There 42 possible combinations for the pizza previous quiz
- 8. A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles? your turn!
- 9. No. of ways in selecting fountain pen = 10 No. of ways in selecting ball pen = 12 No. of ways in selecting pencil = 5 Total number of selecting all these = 10 x 12 x 5 = 600 sample PROBLEM
- 11. It is a counting technique that determines the number of possible arrangements in a collection of items where the order of the selection matters. permutation The word 'distinct' means that the objects of a set must be all different. There shall be no repetition of occurrence. distinct objects
- 12. Choosing a president, a vice president, a secretary and a treasurer from the 12 members in a club Arranging 3 different mathematics of books in a shelf Getting the possible arrangements of letters of READ permutation of distinct objects EXAMPLES: It refers to the different arrangements of distinct objects in a line. It is the different arrangements when no objects are identical or the same.
- 13. How many possible arrangements could be made when selecting a president, a vice president, a secretary and a treasurer from the 12 members in a club sample problem 1
- 14. There are 12 members. No. of ways in selecting: By FCP: (12)(11)(10)(9) = 11, 880 a. president: 12 b. vice-president: 11 c. secretary: 10 d. treasurer: 9 Thus, there are 11, 880 ways to arrange 12 members of the club for the position P, VP, S andT. SOLUTION
- 15. A librarian wanted to organize a book shelf. In how many arrangements can be made with 3 different mathematics books? sample problem 2
- 16. There are 3 different mathematics books. No. of ways in selecting: By FCP: (3)(2)(1) = 6 a. 1st book: 3 b. 2nd book: 2 c. 3rd book: 1 Thus, there are 6 ways to arrange 3 different mathematics books in a shelf. SOLUTION
- 17. In how many ways can you arrangement the letters of the word READ? sample problem 3
- 18. There are 4 different letters of the word READ No. of ways in selecting: By FCP: (4)(3)(2)(1) = 24 a. 1st letter: 4 b. 2nd letter: 3 c. 3rd letter: 2 d. 4th letter: 1 Thus, there are 24 ways to arrange the letters of the word READ. SOLUTION
- 19. RECALL a. Sample Problem 2 solution: (3)(2)(1) = 6 b. Sample Problem 3 solution: (4)(3)(2)(1) = 24 It means to multiply all whole numbers from the chosen number down to 1. In symbols, " ! " This operation is called Factorial.
- 20. Take note 3! = (3)(2)(1) = 6 4! = (4)(3)(2)(1) = 24 7! = (7)(6)(5)(4)(3)(2)(1) = 5040 Factorial (!) means to multiply all whole numbers from the chosen number down to 1. Examples:
- 21. calculator
- 22. Take note Anagram is a word or phrase created by rearranging all the letters of a certain word. The letters must be used only once and the word that is formed has meaning. Examples: READ DEAR DARE
- 23. How many anagrams of the word SHARE are there? sample problem 4
- 24. answer HARES SHEAR SHAER HEARS RHEAS -a large flightless bird resembling a small ostrich -to receive a sound -to remove fleece or hair by clipping or cutting -a fast-running, long-eared mammal that resembles a large rabbit -a limited amount There are 5 anagrams of the word SHARE. Anagrams of SHARE are:
- 25. permutation of distinct objects All objects are different. No objects are identical or the same Can be solved using the Fundamental Counting Principle Can be solved using Factorial May use the concept of Anagrams
- 26. Answer the exercises on your worksheet. You may use a calculator to solve for factorial. activity