Vinluan-Jer000000000ome-T.-WEEK-5.1.pptx

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1. Remember me?

2. Activity: WHAT AM I! Instruction: Determine whether each of the following situations involves permutations and combinations. The group who will gain the highest score will win the game. TAKE NOTE: Answer ACCURATELY!

3. LEARNING OBJECTIVES 01 At the end of the lesson, the students should able to: differentiate situations that involve permutations and combinations; 2 3 solve problems that involve permutations and combinations; value accumulated knowledge as means of new understanding.

4. Jerome T. Vinluan (Practice Teacher) Solving Problems Involving Permutations and Combinations Pangasinan State University Bayambang Campus College of Teacher Education Science and Mathematics Department Bayambang , Pangasinan

5. Isabel’s Treat

6. PERMUTATIONS n P r =   COMBINATIONS n C r =   1. Seven friends Brand Kirby, Dance Kate, Rahim, Arian, Ruie , Jhian , Micah, and Carl, leave at Isabel’s Treat. Each person says good-bye to each of the others with a fist bump. How many fist bumps are needed? Given: n = 7 r = 2 7 C 2 = ? Solution: 7 C 2 =   7 C 2 =   7 C 2 =   7 C 2 =   7 C 2 =   Therefore, the number of fist bumps is 21. COMBINATION

7. PERMUTATIONS n P r =   COMBINATIONS n C r =   2 . Kirby has 12 modules to answer this week. In how many different ways can he pick a first, second, and third module to answer on Monday? Given: n = 12 r = 3 12 P 3 = ? Solution: 12 P 3 =   12 P 3 =   12 P 3 = 12 (11) (10) 12 P 3 =   Therefore, there are 1320 different ways to do it. PERMUTATION

8. PERMUTATIONS n P r =   COMBINATIONS n C r =   3 . Abrahim wants to solve a system of equations through elimination by combining any two equations. The number of equations he has is equal to the number of variables. He realizes that He has 10 possible ways to start his solution How many equations does he have? Given: n = ? r = 2 n C r = 10 Solution: n C r =   10 =   10 =   10 (2) =   20 =   Therefore, there are 5 equations. COMBINATION 5 (4) =   n =  

9. Activity: A-PAIR TAYO! (WORK SILENTLY) Solve the following problems. 1. There are 11 different ulam in KuMAIN’s Eatery today. A customer is asked to get certain number of ulam . If the customer has 165 possible ways as a result, how many ulam did he buy?   2. In a town fiesta orchestra competition with 12 performers, in how many ways can the organizer arrange the first three performers ? 3. In a room, there are 10 chairs in a row. In how many ways can 5 students be seated in consecutive chairs?

10. PERMUTATIONS n P r =   COMBINATIONS n C r =   4 . Marian would like to invite 9 friends to go on a trip but has room for 6 of them. In how many ways can they be chosen. Given: n = 9 r = 6 n C r = ? Solution: n C r =   n C r =   n C r =   n C r =   n C r = 8 4 Therefore, there are 84 ways. COMBINATION

11. 5 . Find the numbers of different ways of placing 8 marbles in a row given that 3 are red, 2 are green, 2 yellow, and 1 is black . Given: n = 8 p = 3 q = 2 r = 2 s = 1 P = ? Solution: P =   P =   P =   Therefore, there are 1 , 680 different ways. DISTINGUISHABLE PERMUTATION DISTINGUISHABLE PERMUTATION P =  

12. PERMUTATIONS n P r =   COMBINATIONS n C r =   6 . How many ways can 4 officers in Grade 10 – Amethyst class be elected among 33 students. Given: n = 33 r = 4 n C r = ? Solution: n C r =   33 C 4 =   33 C 4 =   33 C 4 =   33 C 4 =   Therefore, there are 40, 920 ways. COMBINATION

13. 7. In a round table, how many ways can 8 different colored chairs be arranged? Given: n = 8 P = ? Solution: P = (n-1)! P = (8-1 )! P = 7 ! P = 5,040 Therefore, there are 5,040 ways. CIRCULAR PERMUTATION CIRCULAR PERMUTATION P = (n-1)!

14. PERMUTATIONS n P r =   COMBINATIONS n C r =   8 . An exhibition hall has eight doors. In how many ways can you enter and leave the hall through different doors ? Given: n = 8 r = 2 8 P 2 = ? Solution: 8 P 2 =   8 P 2 =   8 P 2 = 56 Therefore, there are 56 ways to do it. PERMUTATION

15. PERMUTATIONS n P r =   COMBINATIONS n C r =   9 . 7/11 has 10 different flavors of donut. Khim wants to buy one order with 3 different flavors. How many different selections are possible? Given: n = 10 r = 3 n C r = ? Solution: n C r =   10 C 3 =   10 C 3 =   10 C 3 =   10 C 3 = 1   Therefore, there are 1 20 ways. COMBINATION

16. WAG KA NG MAGPALIWANAG! Instruction: The teaching intern will give a situation on problems involving permutations or combinations. The student will have a freedom in explaining their side or opinion regarding to the situation given.

17. Situation: You want to secure your travel bag with a “combination” lock that has a 4-digit code and you want to put in a code that has no repeated numbers. Which counting technique is involved in the problem, permutations or combinations? Explain your reasoning.

18. ENCAPSULATE ME!

19. MATH Advice! a M essage of A spiration , T hought, and H ope

20. “Life is full of permutations and combinations . Sometimes the order you do things matter sometimes it doesn’t, but in order to find the solution in life you must work through each possibility presented to find your opportunity.” ~Gregory Willis

21. THANK YOU FOR LISTENING, GRADE 10!