If we have 100 (identical) tennis balls and 40 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) 20 of the bags can only contain an even number of tennis balls (the other 20 bags can contain any number of tennis balls).

A First Course in Probability (10th Edition)
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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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This question is from the subject Discrete Mathematics 2, where it involves basic set theory, combinatorics, graph theory etc.

2. If we have 100 (identical) tennis balls and 40 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) 20 of the bags can only contain an even number of tennis balls (the other 20 bags can
contain any number of tennis balls).
Transcribed Image Text:2. If we have 100 (identical) tennis balls and 40 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) 20 of the bags can only contain an even number of tennis balls (the other 20 bags can contain any number of tennis balls).
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