1. **Problem:** How many ways can you make a 4-topping pizza if there are 12 toppings to choose from? 2. **Formula:** This is a combination problem because the order of toppings does not matter. The number of ways to choose $k$ toppings from $n$ options is given by the combination formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Apply values:** Here, $n=12$ and $k=4$. $$\binom{12}{4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!}$$ 4. **Calculate factorials:** $$12! = 12 \times 11 \times 10 \times 9 \times 8!$$ So, $$\binom{12}{4} = \frac{12 \times 11 \times 10 \times 9 \times \cancel{8!}}{4! \times \cancel{8!}} = \frac{12 \times 11 \times 10 \times 9}{4!}$$ 5. **Calculate $4!$:** $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 6. **Simplify numerator and denominator:** $$\frac{12 \times 11 \times 10 \times 9}{24}$$ Calculate numerator: $$12 \times 11 = 132$$ $$132 \times 10 = 1320$$ $$1320 \times 9 = 11880$$ So, $$\frac{11880}{24}$$ 7. **Divide:** $$\frac{11880}{24} = 495$$ **Answer:** There are 495 ways to make a 4-topping pizza from 12 toppings. **Final answer: 495**