4. A car dealership has 5 minis (M), 8 convertibles (C) and 14 sedans (S) in its inventory. Throughout this problem, assume that the unordered/ordered lists cannot include duplicates. (a) An unordered list of 20 cars is a combination of 20 cars from this car dealership where the order does not matter, that is to say that if two lists include the same 20 cars they are considered to be the same unordered lists. How many unordered lists of 20 cars can be created in which no car is displayed more than once? (b) If you create an unordered list of 20 cars completely at random (that is, any car is equally likely to be picked), what is the probability that the list includes all 8 convertibles? (c) An ordered list of 4 cars is a sequence of 4 cars from this car dealership where the cars are displayed in a specific order, that is to say that two lists including the same 4 cars in a different order are considered different ordered lists. How many ordered lists of 4 cars can be created in which no car is displayed more than once?
4. A car dealership has 5 minis (M), 8 convertibles (C) and 14 sedans (S) in its inventory. Throughout this problem, assume that the unordered/ordered lists cannot include duplicates. (a) An unordered list of 20 cars is a combination of 20 cars from this car dealership where the order does not matter, that is to say that if two lists include the same 20 cars they are considered to be the same unordered lists. How many unordered lists of 20 cars can be created in which no car is displayed more than once? (b) If you create an unordered list of 20 cars completely at random (that is, any car is equally likely to be picked), what is the probability that the list includes all 8 convertibles? (c) An ordered list of 4 cars is a sequence of 4 cars from this car dealership where the cars are displayed in a specific order, that is to say that two lists including the same 4 cars in a different order are considered different ordered lists. How many ordered lists of 4 cars can be created in which no car is displayed more than once?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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