Street Combinatorics - 6 by 7 grid

Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.

This is equivalent to the problem

nnnnnnneeeeee

How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $${13\choose6}=\frac{13!}{6!7!}=\color{red}{1716}$$

Consider this:

You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?

The answer is then $\binom{6+7}6=\binom{13}6=1716$