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Exploring Permutations and Combinations: Key Concepts and Examples

This resource delves into the principles of permutations and combinations, specifically focusing on scenarios where order matters and when it does not. Through practical examples such as arranging keys on a ring, selecting students for a quiz bowl, determining contest placements, planning gym visits, and forming relay pairs, students will learn to apply formulas to find the number of possible arrangements and selections. By using step-by-step calculations and explanations, this guide aids in mastering the concepts of combinatorial mathematics.

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Exploring Permutations and Combinations: Key Concepts and Examples

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  1. PRACTICEwithPermutationsandCombinations

  2. Order Order does matters Not matterDon’t Do divide. Divide. PermutationsCombinations

  3. 1. Find the number of ways that 9 keys can be placed on a key ring. Circular permutation

  4. The formula The numbers The answer 1. Find the number of ways that 9 keys can be placed on a key ring. Circular permutation

  5. The formula n! n The numbers The answer 1. Find the number of ways that 9 keys can be placed on a key ring. Circular permutation

  6. The formula n! n The numbers The answer 1. Find the number of ways that 9 keys can be placed on a key ring. Circular permutation 9! = 9

  7. The formula n! n The numbers The answer 1. Find the number of ways that 9 keys can be placed on a key ring. Circular permutation 9! = 403209

  8. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition?

  9. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition? Order Order does matters? Not matter? Don’t Do divide. Divide.

  10. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition? Order Order does matters? Not matter? Don’t Do divide. Divide.

  11. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition? The numbers Order Order does matters? Not matter? Don’t Divide.divide. The answer

  12. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 21x20x19 3! The answer

  13. 2. In a group of 21 math students, 3 of them will be chosen to go to quiz bowl. In how many ways can the students be chosen for the competition? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 21x20x19 3! The answer 1330

  14. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place?

  15. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place? Order Order does matters? Not matter? Don’t Divide.divide.

  16. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place? Order Order does matters? Not matter? Don’t Divide.divide.

  17. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place? The numbers Order Order does matters? Not matter? Don’t Divide.divide. The answer

  18. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 50 x 49 The answer

  19. 3. 50 kids enter a contest. In how many ways can they finish in first place and second place? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 50 x 49 The answer 2450

  20. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible?

  21. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible? Order Order does matters? Not matter? Don’t Divide.divide.

  22. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible? Order Order does matters? Not matter? Don’t Divide.divide.

  23. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. The answer

  24. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 7x6x5 3! The answer

  25. 4. The health club gym is open every day. If you are on a certain plan, you can only go 3 days a week. How many 3-day combinations are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 7x6x5 3! The answer 35

  26. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible?

  27. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible? Order Order does matters? Not matter? Don’t Divide.divide.

  28. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible? Order Order does matters? Not matter? Don’t Divide.divide.

  29. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. The answer

  30. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 30 x 29 2! The answer

  31. 5. On Field Day, class groups compete with each other. In the 4th grade class, 30 kids must be paired to run a relay. How many pairings are possible? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 30 x 29 2! The answer 435

  32. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students?

  33. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students? Order Order does matters? Not matter? Don’t Divide.divide.

  34. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students? Order Order does matters? Not matter? Don’t Divide.divide.

  35. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students? The numbers Order Order does matters? Not matter? Don’t Divide.divide. The answer

  36. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 145 x 144 The answer

  37. 6. In how many ways can a valedictorian and a salutatorian be chosen from a graduating class of 145 students? The numbers Order Order does matters? Not matter? Don’t Divide.divide. 145 x 144 The answer 20880

  38. The End

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