Question

How many ways are there to walk in xy space from the point (0,0) to (2,3) in exactly 5 steps if in each step, you walk 1 unit along the x or y axis only going in the positive direction?

Answer 1

Answer:

Therefore there are 10 ways to walk in xy space from (0,0) to (2,3).

Step-by-step explanation:

To move from (0,0) to (2,3) one has to walk 2 step along x-axis and 3 steps along y-axis.

One can chose 2 steps along x-axis and then 3 steps along y axis

Or,

2 steps along y-axis ,1 step along x-axis , 1 step along y-axis,1 step along x-axis

And so on.

This is a permutation of(2+3) things where 2 and 3 are two types of kinds.

The required permutation is   $\frac{(2+3)!}{2!3!}=\frac{5!}{2!3!} =10$  

Therefore there are 10 ways to walk in xy space from (0,0) to (2,3).