Answer:
The number of path we can take to walk from A to B via a 7 unit path while staying on the grid is 35 paths
Explanation:
Given that we are to walk via a 7 unit path, we have;
Path to walk = Right or Left from start point A
Total number of rights and left to get to point B from A must be= 7
Left direction=3 turns
Right direction=4 turns
Number of ways for the first turn = 7, the next turn has 6 ways after that 5, then 4 next, 3 next, 2 next and 1
7 × 6 × 5 × 4 × 3 × 2 × 1 out of which
four are in the right direction in 4 × 3 × 2 × 1 ways and
3 are in the left direction in 3 × 2 × 1 ways,
Number of ways=7! / 4!3!
=7*6*5*4*3*2*1 / 4*3*2*1*3*2*1
=5040/144
=35