Consider a chain with N >> 1 segments of length 1. One end of the chain is at the origin, the other at a point R. In this onedimensional model the segments may face left or right. The number of segments facing right is n.
1: What is the number of possible configurations in the chain? [This I have answered, 2^N]
2: Find the number of configurations with n segments facing right? Which is the associated R(n)? [Did first part, C(N, n)]
The Attempt at a Solution
I frankly don't get what the hell R(n) is supposed to be. The answer is R(n) = 2(n - N/2)
Analyzing that I concluded that R(n) is 0 if the number segments facing left = number of segments facing right. Othewise the length of R(n) is [number of right facing segments - number of left facing segments] * 2. Which tells me just about nothing, what on Earth is R(n) supposed to represent? I was thinking maybe the left segments 'take out' the right segments and R(n) represents what's left, but that doesn't explain the factor 2 because every segment is of length 1.
Thanks in advance.
Edit: Think I figured it out. Was right with initial thinking after all