Y by Adventure10, megarnie, Mango247
Let
be an integer. A path from
to
in the
plane is a chain of consecutive unit moves either to the right (move denoted by
) or upwards (move denoted by
), all the moves being made inside the half-plane
. A step in a path is the occurence of two consecutive moves of the form
. Show that the number of paths from
to
that contain exactly
steps
is
![\[\frac{1}{s} \binom{n-1}{s-1} \binom{n}{s-1}.\]](//latex.artofproblemsolving.com/f/2/1/f2170eca57a41dec920002f4157e9afe25165aa8.png)












![\[\frac{1}{s} \binom{n-1}{s-1} \binom{n}{s-1}.\]](http://latex.artofproblemsolving.com/f/2/1/f2170eca57a41dec920002f4157e9afe25165aa8.png)
This post has been edited 1 time. Last edited by orl, Nov 14, 2004, 10:27 PM