Summary
Permutations and combinations are mathematical concepts used to solve problems involving arrangements and selections. Factorial Function — the product of all positive integers from 1 to n, denoted as n!. Example: 3! = 3 × 2 × 1 = 6. Permutation — an arrangement of objects where order matters. Example: Arranging A, B, C in different orders like ABC, ACB, BAC. Combination — a selection of objects where order does not matter. Example: Choosing 2 letters from A, B, C like AB, AC, BC.
Exam Tips
Key Definitions to Remember
- Factorial: The product of all positive integers up to a given number.
- Permutation: Arrangement of objects where order is important.
- Combination: Selection of objects where order is not important.
Common Confusions
- Mixing up permutations and combinations.
- Forgetting to divide by factorials of repeated items in permutations with repetition.
Typical Exam Questions
- How many ways can 5 people be arranged in a line? Answer: 5! = 120 ways.
- How many ways can you choose 3 fruits from 5 different fruits? Answer: = 10 ways.
- How many distinct arrangements of the word 'BANANA'? Answer: = 120 ways.
What Examiners Usually Test
- Understanding of when to use permutations vs combinations.
- Ability to calculate permutations and combinations accurately.
- Application of factorials in solving arrangement problems.