Q3-Lesson-4-Permutations-vs-Combinations (5).pptx

Q3-Lesson-4-Permutations-vs-Combinations (5).pptx

1. Q3 Lesson 4

2. At the end of this lesson, you should be able to differentiates permutation from combination of n objects taken r at a time. Objectives

3. ACTIVITY Determine whether each situation involves a permutation or a combination . 1. Five badminton players chosen from a group of 9 2. Seven toppings for a pizza 3. A classroom seating arrangement 4. 15 books in a library shelf 5. Choosing a class president, vice president, and a secretary 6. Eight outfits chosen from fifteen outfits to be modeled

4. Study the tasks or activities that follow, and then answer the questions below. 1. In which tasks/activities is order or arrangement important? 2. In which task/activities is order not important? Activity: Put Some Order Here

5. Choosing 5 questions to answer out of 10 questions in a test. Opening a combination lock Winning in a contest Selecting 7 people to form a Student Affairs Committee Forming triangles from 6 distinct points in which no 3 points are collinear. Assigning seats to guests at dinner Drawing a set of 6 numbers in a lottery containing numbers 1 to 45 Entering the PIN (Personal Identification Number) of your ATM card Selecting 3 posters to hang out of 6 different posters. Listing the elements of subsets of a given set Activity: Put Some Order Here

6. Identify if the problem illustrates permutation or illustrates combination . Exercises : Collect and Select… and Arrange! In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other? permutation  

7. Identify if the problem illustrates permutation or illustrates combination . Exercises : Collect and Select… and Arrange! In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done? combination  

8. Identify if the problem illustrates permutation or illustrates combination . Exercises : Collect and Select… and Arrange! A soloist is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice? combination  

9. Identify if the problem illustrates permutation or illustrates combination . Exercises : Collect and Select… and Arrange! In a certain general assembly, three major prizes are at stake. In how many ways can the first, second, and third prizes can be drawn from the box containing 120 names? permutation  

10. A jar contains 5 red marbles, 7 green marbles, and 6 yellow marbles. In how many ways can 6 marbles be chosen if there should be 2 marbles of each color? Example Solution : ____ ____ ____   = 3,150 COMBINATIONS 5 C 2 7 C 2 There are 3,150 ways can 6 marbles be chosen with 2 balls of each color 6 C 2

11. How many numbers greater than 4,000 can be formed from the digits 2, 3, 4, 5, and 6? Example Solution : ____ ____ ____   = 192 PERMUTATIONS 5 P 5 3 P 1 There are 192 numbers greater than 4,000 can be formed 4 P 3 5 P 5 → 5-digit 3 P 1 4 P 3 → 4-digit  

12. Determine whether each situation involves a permutations or a combinations . First-five players chosen from a basketball team Seven toppings for ice cream Finding the diagonals of a polygon A classroom sitting arrangement 32 books on a 2-layer shelf Choosing officers in a class Eight outfits chosen from fifteen outfits to be modeled A six-person committee from your math class Assembling a jigsaw puzzle Four people posing for pictures Written Works 3.4

13. Determine whether each situation involves a permutations or a combinations . combinations combinations combinations permutations permutations combinations combinations combinations permutations permutations Written Works 3.4

14. Determine whether each situation involves a permutations or a combinations . Seven toppings for pizza Six members chosen from a mathematics club A meeting in a conference hall Choosing a representative in spelling bee Eight outfits chosen from fifteen outfits to be modeled Finding the diagonals of a hexagon Three sets of encyclopedia on a 3-layer shelf Schedule of classroom cleaners A classroom picture taking Playing a Lego puzzle Written Works 3.4