You have decided to go on a (very foolish) diet. Specifically, you have chosen to eat only nuts, consisting of peanuts, almonds, walnuts, and cashews. 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, peanuts and walnuts on Wednesday, and so on. How many different dietary plans could you have for a given week? 2. Now suppose that each day you eat 3 meals. You also decide to eat three types of nuts each day, and that you will eat one kind of nut for each of your three meals. Additionally, 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 each day but you are easily bored, and decide that you will never eat the same nuts at the same times for two or more days of the week. How many different dietary plans could you have for a given week under this new scheme?
You have decided to go on a (very foolish) diet. Specifically, you have chosen to eat only nuts, consisting of peanuts, almonds, walnuts, and cashews. 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, peanuts and walnuts on Wednesday, and so on. How many different dietary plans could you have for a given week? 2. Now suppose that each day you eat 3 meals. You also decide to eat three types of nuts each day, and that you will eat one kind of nut for each of your three meals. Additionally, 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 each day but you are easily bored, and decide that you will never eat the same nuts at the same times for two or more days of the week. How many different dietary plans could you have for a given week under this new scheme?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:You have decided to go on a (very foolish) diet. Specifically, you have chosen to eat
only nuts, consisting of peanuts, almonds, walnuts, and cashews.
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, peanuts and walnuts on Wednesday,
and so on. How many different dietary plans could you have for a given week?
2. Now suppose that each day you eat 3 meals. You also decide to eat three types of
nuts each day, and that you will eat one kind of nut for each of your three meals.
Additionally, 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
each day but you are easily bored, and decide that you will never eat the same
nuts at the same times for two or more days of the week. How many different
dietary plans could you have for a given week under this new scheme?
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