A robot traveling from point (0, 0) to point (6, 8) must take eight steps to the right, and six steps down. This can be represented as a string like so:

`RRRRRRRRDDDDDD`

Where R represents a step to the right, and D represents a step down. The number of ways to traverse the entire grid in the described manner is the number of permutations of the above 14-character string.

There are initially 14! permutations of the string. However, no distinction can be made between any of eight R’s and any of the six D’s, so the number of permutations has to be scaled down by the number of permutations of R’s and the number of permutations of D’s.

The answer is:

`\frac{14!}{6!8!} = 3,003 6!8! 14! =3,003`

There are 3,003 ways to traverse the grid.

If the grid is 8 X 6, wouldn’t that be **seven** steps to the right, and **five** steps down?

```
12! / 5! * 7!
=> 12 * 11 * 10 * 9 * 8 * 7! / 5! * 7!
=> 12 * 11 * 10 * 9 * 8 / 5!
=> 11 * 9 * 8
= 792
```