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Use generating functions to determine the number of different ways 32 identical stuffed animals can be given to five children so that each child receives at least two but no more than 10 stuffed animals. Hint: Recall that if x is a real number with |x| < 1 and n a positive integer we have n+k- (1 − x)¯" = Σ(" - Σ (₁+1-¹) ² = k k=0

Use generating functions to determine the number of different ways 32 identical stuffed animals can be given to five children so that each child receives at least two but no more than 10 stuffed animals. Hint: Recall that if x is a real number with |x| < 1 and n a positive integer we have n+k- (1 − x)¯" = Σ(" - Σ (₁+1-¹) ² = k k=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use generating functions to determine the number of different ways 32 identical stuffed animals can be given to five children so that each child receives at least two but no more than 10 stuffed animals. Hint: Recall that if x is a real number with |x| < 1 and n a positive integer we have (1 − x)¯" = discrete math n+k -Σ(1) (1² + k − 1) ₂2². k k=0
Transcribed Image Text:Use generating functions to determine the number of different ways 32 identical stuffed animals can be given to five children so that each child receives at least two but no more than 10 stuffed animals. Hint: Recall that if x is a real number with |x| < 1 and n a positive integer we have (1 − x)¯" = discrete math n+k -Σ(1) (1² + k − 1) ₂2². k k=0
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