Question

Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?

Answer 1

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

Step-by-step 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