1. **Problem Statement:** Understand real-life scenarios involving permutations and combinations. 2. **Permutations Scenario:** Suppose you want to arrange 3 different books on a shelf. The number of ways to arrange them is a permutation because order matters. 3. **Calculation:** The number of permutations of 3 books is $$3! = 3 \times 2 \times 1 = 6$$. 4. **Explanation:** Each different order counts as a unique arrangement, so the order is important. 5. **Combinations Scenario:** Imagine you have 5 different fruits and want to select 2 to make a fruit salad. The order of selection does not matter here. 6. **Calculation:** The number of combinations is $$\binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10$$. 7. **Explanation:** Since the order does not matter, selecting apple then banana is the same as banana then apple. 8. **Summary:** Permutations are used when order matters, combinations when order does not matter. These scenarios help understand how to count arrangements and selections in everyday situations.