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) the bags are required to be non-empty; ) we allow bags to be empty; ) all bags are required to be non-empty, 10 of the bags can only c

) the bags are required to be non-empty; ) we allow bags to be empty; ) all bags are required to be non-empty, 10 of the bags can only c

Linear Algebra: A Modern Introduction
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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3. If we have 80 (identical) tennis balls and 20 identical bags to place them in, how many ways are there to distribute the tennis balls into the bags if (a) the bags are required to be non-empty; (b) we allow bags to be empty; (c) all bags are required to be non-empty, 10 of the bags can only contain an odd number of tennis balls and the remaining 10 bags can only contain an even number of tennis balls. (Hint: for (c) introduce a parameter (t say) to count the number of balls put in the odd bags.)
Transcribed Image Text:3. If we have 80 (identical) tennis balls and 20 identical bags to place them in, how many ways are there to distribute the tennis balls into the bags if (a) the bags are required to be non-empty; (b) we allow bags to be empty; (c) all bags are required to be non-empty, 10 of the bags can only contain an odd number of tennis balls and the remaining 10 bags can only contain an even number of tennis balls. (Hint: for (c) introduce a parameter (t say) to count the number of balls put in the odd bags.)
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