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In how many ways can they line up so that no two geese are standing next to one another? (There is always at least one duck between any two geese.) In how many ways can they line up so that every goose is standing next to exactly one other goose?

In how many ways can they line up so that no two geese are standing next to one another? (There is always at least one duck between any two geese.) In how many ways can they line up so that every goose is standing next to exactly one other goose?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Discrete Math:

Suppose there are 10 ducks and 6 geese that are lined up in a single row. Look at the image attached below to answer the questions.

 

 

a. In how many ways can they line up so that no two geese are standing next to one another? (There is always at least one duck between any two geese.) b. In how many ways can they line up so that every goose is standing next to exactly one other goose?
Transcribed Image Text:a. In how many ways can they line up so that no two geese are standing next to one another? (There is always at least one duck between any two geese.) b. In how many ways can they line up so that every goose is standing next to exactly one other goose?
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There are 10 ducks and 6 geese.

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