Question 1178806
Absolutely! Let's address this scenario:

**1. Diverse Food Choices for Mr. Agustin's Restaurant (Considering Health & Nutrition):**

Here's a list of food choices categorized to provide variety and address nutritional needs:

**Soups:**

* **Chicken Noodle Soup:** Classic, comforting, and provides protein.
* **Vegetable Minestrone:** High in fiber and vitamins, a good vegetarian option.
* **Lentil Soup:** Rich in protein and iron, hearty and filling.
* **Butternut Squash Soup:** Creamy, with vitamin A and fiber.

**Meat Dishes:**

* **Grilled Chicken Breast:** Lean protein, versatile.
* **Baked Salmon:** Rich in omega-3 fatty acids, healthy fats.
* **Lean Beef Stir-Fry:** Protein and vegetables, customizable.
* **Turkey Meatloaf:** Leaner alternative to beef meatloaf.

**Fish Dishes:**

* **Baked Cod with Lemon and Herbs:** Light and flaky, low in fat.
* **Grilled Tilapia:** Mild flavor, good source of protein.
* **Shrimp Scampi (with whole-wheat pasta):** Seafood option, can be made healthier.

**Vegetables:**

* **Steamed Broccoli:** High in vitamins C and K, fiber.
* **Roasted Asparagus:** Antioxidants, vitamins, and minerals.
* **Mixed Green Salad:** Customizable, leafy greens, and various vegetables.
* **Sautéed Spinach:** Iron, vitamins, and minerals.

**Fruits:**

* **Fresh Fruit Salad:** Variety of seasonal fruits.
* **Baked Apples with Cinnamon:** Natural sweetness, fiber.
* **Berry Parfait (with yogurt):** Protein and antioxidants.
* **Orange Slices:** Vitamin C.

**Desserts:**

* **Fruit Sorbet:** Light and refreshing.
* **Greek Yogurt with Honey and Nuts:** Protein and healthy fats.
* **Whole-Wheat Apple Crisp (with less sugar):** Whole grains and fiber.
* **Dark Chocolate (small portion):** Antioxidants.

**Beverages:**

* **Water (infused with fruit or herbs):** Hydration.
* **Unsweetened Iced Tea:** Refreshing, low in calories.
* **Freshly Squeezed Juices (limited portions):** Vitamins.
* **Herbal Teas:** Variety of flavors, caffeine-free.

**2. Permutation and Combination Problems:**

**Problem 1 (Permutation):**

* **Scenario:** Mr. Agustin wants to create a daily special that consists of a soup, a meat dish, and a vegetable. He has 3 soup options, 4 meat dish options, and 5 vegetable options. How many different daily specials can he create if the order of the courses matters?
* **Solution:**
    * This is a permutation problem because the order matters (soup, then meat, then vegetable).
    * Number of permutations = (Number of soup options) * (Number of meat options) * (Number of vegetable options)
    * Number of permutations = 3 * 4 * 5 = 60
    * **Answer:** Mr. Agustin can create 60 different daily specials.

**Problem 2 (Combination):**

* **Scenario:** A customer wants to create a side dish that consists of 3 different vegetables from the 5 vegetable options available. How many different side dish combinations can the customer create?
* **Solution:**
    * This is a combination problem because the order of the vegetables doesn't matter.
    * Number of combinations = nCr = n! / (r! * (n-r)!)
        * n = 5 (total vegetable options)
        * r = 3 (vegetables to choose)
    * Number of combinations = 5! / (3! * 2!) = (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1)) = 120 / (6 * 2) = 120 / 12 = 10
    * **Answer:** The customer can create 10 different side dish combinations.