title: Robot moving in a grid algorithm possible paths and time complexity ?
body: <p>I'm not able to understand how for the problem below the number of paths are (x+y)!/x!y! .. I understand it comes from choose X items out of a path of X+Y items, but why is it not choosing x items over x+y + choosing y items over x+y ? Why does it have to be only x ? </p>
  
  <blockquote>
    <p>A robot is located at the top-left corner of a m x n grid (marked
    ‘Start’ in the diagram below). The robot can only move either down or
    right at any point in time. The robot is trying to reach the
    bottom-right corner of the grid (marked ‘Finish’ in the diagram
    below). How many possible paths are there?</p>
  </blockquote>
  
  <ol>
  <li>Are all of these paths unique ? </li>
  <li>How do I determine that ? </li>
  <li>And what would be the time complexity for the backtracking algorithm ? </li>
  </ol>