Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at then it can move to either or .
How many distinct paths are there for the robot to reach the point starting from the initial position ?
View worked solution
Answer: A
To reach the destination starting from , the robot must make exactly:
- steps to the Right (), since the -coordinate increases from to .
- steps Up (), since the -coordinate increases from to .
Thus, any valid path consists of a sequence of exactly steps, containing exactly '' moves and '' moves.
The number of distinct paths is the number of ways to arrange these moves. This is equivalent to choosing the positions for the '' moves out of the total available positions:
Therefore, the correct option is A.
Free practice · Your answers on this page are not saved.