Final demonstration about combination in grade 10

Combination

1. COMBINATION MATHEMATICS 10 JEADEN G. MARABE

2. Review! Identify which situations illustrate permutation and combination? Choosing four of your friends to attend your debut. Unlocking a combination lock. Picking 6 balls from a basket of 15 balls. Determining the top three winners in a Math Quiz Bee. Choosing 5 questions to answer out of 10 questions.

3. Answer! COMBINATION PERMUTATION COMBINATION PERMUTATION COMBINATION

4. “MINI-LOTTO” MECHANICS OF THE GAME You are going to choose 5 numbers out of those 10 numbers. I will draw 5 numbers at random. Those player/s who have a matching 5 numbers against the numbers I draw will have the grand prize. Take note that the numbers are in any order. In case there is a tie, the winners will share for the grand prize. For those students have matching of 4 numbers from the numbers I drew will have the second prize. For 3 numbers, they will have the third prize.

5. COMBINATION MATHEMATICS 10

6. Learning Objectives a.) differentiate permutation and combination. c.) appreciate the usefulness of combination in real life situations. b.) solve probability of ‘n’ objects using combination; and

7. Combination refers to the number of ways of selecting objects from a set when order is not important.

8. Notation of Combination The number of combinations of n objects taken e at a time is denoted by: C( n,r ), n C r , or C )

9. Suppose now, that you are asked to form different triangles out of 4 points plotted, say, A, B, C, and D, of which no three are collinear. We can see that ∆ABC is the same as ∆BCA and ∆CBA. In the same manner, ∆BCD is the same as ∆CBD and ∆DBC. This is another illustration of combination. The different triangles that can be formed are ∆ABC, ∆ABD, ∆BCD, and ∆CDA. Thus, three are 4 combinations.

10. ACB ABD BCD CDA ACB ADB BDC CAD BCA BDA CDB DAC BAC BAD CBD DCA CAB DBA DBC ADC CBA DAB DCB ACD

11. There are 24 possibilities. Since you learned in Geometry that we can name a triangle using three vertices in any order, then if we look more closely, we can see that all the triangles in the same column are identical. Thus, the actual number of combination is

12. Note: There are 4 objects (A, B, C, D) n=4 They are selected 3 at a time r=3 And so, equation (1) becomes C(n, r) = . Since P(n, r) = Then C(n, r) = = =

13. The combination of n objects taken r at a time is:   C(n, r) =

14. Example 1 In how many ways can a committee consisting of 4 members be formed from 8 people?

15. Example 1 In how many ways can a committee consisting of 4 members be formed from 8 people? Solution: n = 8 , r = 4 C(n, r) = C(8, 4) = = = = 7 = 70 ways

16. Example In a culinary arts class, a student is asked to select dishes from a list of 10. How many ways can he or she select 7?

17. Example In a culinary arts class, a student is asked to select dishes from a list of 10. How many ways can he or she select 7? Solution: n = 10 , r = 7 C(n, r) = C(10, 7) = = = = 10 = 120 ways

18. GROUP ACTIVITY Group 1: A committee of 6 officials is to be chosen from 8 board of directors. How many ways can it be chosen? Group 2: In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve?

19. GROUP ACTIVITY Criteria Outstanding (5 points) Satisfactory (3 points) Fair (1 point) Accuracy All answers are correct. Some answers are correct. All answers are not correct. Presentation The presentation was clear. The presentation was not that clear. The presentation was not clear. Teamwork The group clearly worked together with each team member making an important contribution to the output. The group worked together sometimes and some of the members made important contributions to the output. The group failed to work at all. Promptness The group finish before the allotted time. The group finish in the allotted time. The group finish 2-5 mins. after the allotted time. Rubrics for Group Activity/ Cooperative Learning

20. GROUP ACTIVITY Group 2: Group 1:

21. Let's Recall Differentiate Permutation and Combination.   What is the formula for Combination?

22. EVALUATION Solve the following problems using combination.  1.) How many ways can you select a committee of 5 students out of 9 students? 2.) From a box of 10 marbles, in how many ways can you choose 4?

23. ASSIGNMENT  1.) At the library, Ina found 6 books of interest but she can only borrow 4 books. How many possible selections can she make? 2.) A club has 14 members. It has to send a delegation of 5 members to represent them at a particular event. Find the number of possible delegations. 3.) From a population of 30 households, in how many ways can a researcher select a sample size of 15?