) 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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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