You have decided that, instead of eating fruits, you will only eat muts, specifically 4 kinds...

 

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You have decided that, instead of eating fruits, you will only eat muts, specifically 4 kinds of nuts: peanuts, almonds, cashews, and walnuts. 1. You also decide that, each day of the week, you will eat exactly two types of nuts from this list. For example, you might choose to have peanuts and almonds on Monday, cashews and walnuts on Tuesday, and peanuts and walnuts on Wednesday, and so on. How many different dietary plans could you have for a given week? In this problem, a "dietary plan" refers to a plan for which two nuts to eat each day for the entire week. 2. Now suppose that each day you eat 3 meals (breakfast, lunch, and dinner). You also decide to eat three types of nuts each day (instead of 2), and that you will eat one type of nut for each of your three meals (breakfast, lunch, and dinner). For example, you might have peanuts for breakfast, walnuts for lunch, and almonds for dinner. This is now a different dietary plan than if you had walnuts for breakfast, almonds for lunch, and peanuts for dinner. (Note that you can't have the same nut for more than one meal on a given day.) How many different dietary plans could you have for a given week under this new scheme? 3. Lastly, assume that you are still eating three types of nuts each day, for 3 meals a day, but you are easily bored, and decide you will never eat the same nuts at the same times for two or more days of the week (for example, you would not have peanuts for breakfast, walnuts for lunch, and almonds for dinner on Tuesday and Friday). How many different dietary plans could you have for a given week under this new scheme? You have decided that, instead of eating fruits, you will only eat muts, specifically 4 kinds of nuts: peanuts, almonds, cashews, and walnuts. 1. You also decide that, each day of the week, you will eat exactly two types of nuts from this list. For example, you might choose to have peanuts and almonds on Monday, cashews and walnuts on Tuesday, and peanuts and walnuts on Wednesday, and so on. How many different dietary plans could you have for a given week? In this problem, a "dietary plan" refers to a plan for which two nuts to eat each day for the entire week. 2. Now suppose that each day you eat 3 meals (breakfast, lunch, and dinner). You also decide to eat three types of nuts each day (instead of 2), and that you will eat one type of nut for each of your three meals (breakfast, lunch, and dinner). For example, you might have peanuts for breakfast, walnuts for lunch, and almonds for dinner. This is now a different dietary plan than if you had walnuts for breakfast, almonds for lunch, and peanuts for dinner. (Note that you can't have the same nut for more than one meal on a given day.) How many different dietary plans could you have for a given week under this new scheme? 3. Lastly, assume that you are still eating three types of nuts each day, for 3 meals a day, but you are easily bored, and decide you will never eat the same nuts at the same times for two or more days of the week (for example, you would not have peanuts for breakfast, walnuts for lunch, and almonds for dinner on Tuesday and Friday). How many different dietary plans could you have for a given week under this new scheme?

Answer rating: 100% (QA)

1 There are 16 different dietary plans that you could have for a given week 2 There are 336 differen... View the full answer