Bean machine (Galton board) explanation I am confused by the marked part of the following explanation (see below; https://en.wikipedia.org/wiki/Bean_machine). Suppose the bead bounces to the right twice and to the left also twice. It will land exactly at the center. But according to this explanation it will land to second bin counting from the left. 
It is also not clear to me, whether by "counting from the left" they mean from the most left or from the center. For similar explanation, see: http://mathworld.wolfram.com/GaltonBoard.html
Can you please reconcile this to me?
Thanks!


It´s a matter of definition how someone counts the bins. In the article of wiki they start with the number zero: $0,1,2,3,...,n$
Quote: 

the number of paths to the $\color{blue}k$th bin on the bottom is given by the
  binomial coefficient ${n\choose \color{blue}k}$.

Therefore the first left bin is denoted by $k=0$. Consequently in the case of $n=4$ the second bin is indeed the center: $01\color{red}234$ 
