Can You Solve This Combinatorics Problem Involving Arrangements of X and Y?

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The discussion focuses on a combinatorics problem involving arrangements of terms x and y in a sequence of n terms, where no two x's can be adjacent. Participants are encouraged to share their attempts and challenges to facilitate assistance. An example illustrates acceptable and unacceptable arrangements based on the given condition. The goal is to generalize the solution for all values of n. Engaging in problem-solving collaboratively is emphasized as a way to enhance understanding.
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given a chain of n terms with each term either being x or y, how many arrangements are there such that you don't have any two terms being x next to each other.

for example if n= 5

(x,y,y,y,x) ; (x,y,x,y,x) are acceptable while (y,x,x,y,x) is not acceptable.

Generalize this result for all values of n.
 
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hi physicsmath94! welcome to pf! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

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