4. 1.55 points | Previous Answers My Notes Ask Your Teacher A restaurant offers

Question

4. 1.55 points | Previous Answers My Notes Ask Your Teacher A restaurant offers 4 different entrees, 5 different vegetables, and 5 different desserts (a) If you are going to order one item from each category, how many different meals are possible? 100 (b) If you are going to order one entree, two different vegetables, and one dessert, how many different meals are possible? 400 (C) How many different meals are possible if you're going to order one entree, three different vegetables, and at most one dessert? In other words you have the option of skipping dessert.) 1200X

Explanation / Answer

b) number of different meals with one entree, two different vegetable and one desert = 4 * 5C2 * 5 = 4 * 5!/(2!*3!) * 5 = 200

c) number of different meals with one entree, three different vegetable and at most one desert = number of different meals with one entree, three different vegetable and zero desert + number of different meals with one entree, three different vegetable and one desert

                                                        = 4 * 5C3 + 4 * 5C3 * 5

                                                        = 4 * 5!/(3!*2!) + 4 * 5!/(3!*2!) * 5

                                                        = 40 + 200

                                                        = 240

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