1. **Problem statement:** You want to buy 5 movies in total: 3 sci-fi and 2 western. The store has 12 sci-fi movies and 8 western movies. How many ways can you choose these movies? 2. **Formula used:** The number of ways to choose $k$ items from $n$ items is given by the combination formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Step 1: Calculate ways to choose 3 sci-fi movies from 12:** $$\binom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!}$$ Calculate factorial values or use simplification: $$= \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220$$ 4. **Step 2: Calculate ways to choose 2 western movies from 8:** $$\binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!}$$ Simplify: $$= \frac{8 \times 7}{2 \times 1} = 28$$ 5. **Step 3: Calculate total ways:** Since the choices are independent, multiply the two results: $$220 \times 28 = 6160$$ **Final answer:** There are **6160** ways to choose 3 sci-fi and 2 western movies from the store.