Q3-Lesson-5-Problems-Involving-Permutations-and-Combinations (3).pptx

Q3-Lesson-5-Problems-Involving-Permutations-and-Combinations (3).pptx

1. Lord, we offer to You our  class  today. We  pray  that through Your Divine Guidance, we would learn how to listen attentively to the inputs of our teacher. May we appreciate his/her effort in imparting his/her knowledge to us. Amen!

2. Problem Solving: Permutations and Combinations Quarter 3 - Lesson 5

3. EXPLOLRATION combination permutation permutation combination permutation

4. EXPLORATIONs Lock A Lock B Lock C permutations permutations combinations

5. illustrations

6. Example 1 . In how many ways can 5 bicycles be parked if there are 7 available parking spaces? permutations Solution: 7 P 5 = 2,520 The 5 bicycles can be parked in 7 available parking space in 2,520 ways.

7. Example 2 . How many ways can the letters of the word MATHEMATICIAN be arranged? distinguishable permutations Solution: = 129,729,600 There are 129,729,600 ways can the letters of MATHEMATICIAN be arranged. 13! 2! 3! 2! 2!  

8. Example 3 . If the sections of Grade 10 class in BNHS must play with the other section in a basketball tournament, how many elimination games will there be? combinations Solution: = 120 There are 120 elimination games. 16 C 2

9. Example 4 . In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they be selected such that at least one boy should be there? combinations Solution: There are 209 ways can four children be selected. 4 boys : 6 C 4 3b & 1g : 6 C 3 4 C 1 2b & 2g : 6 C 2 4 C 2 1b & 3g : 6 C 1 4 C 3   = 15 = 80 = 90 = 24 = 209 10 C 4 – 1 = 209

10. Example 5 . (a) In how many ways can the 12 members of the Board of Directors (BOD) be chosen from 12 parent-nominees and 7 teacher-nominees if there must be 8 parents in the BOD? (b) after the 12 members are chosen, in how many ways can they elect among themselves the top 7 positions (president, vice-president, and others)? combinations and permutations Solution: (a) 12 C 8 7 C 4   = 17,325 (b) 12 P 7 = 3,991,680

11. MASTERMIND

12. MASTERMIND BREAK THE CODE

13. MASTERMIND BREAK THE CODE

14. MASTERMIND BREAK THE CODE