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

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

3 of the turns have to be in the left direction while 4 of the turns are right

Therefore, in 7 turns we have 4 in the right direction and 3 in the left direction which gives;

Number of ways for the first turn = 7, the next turn has 6 ways after that 5 and so on so we have;

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, which gives the number of ways as follows;

`Number \, of \, ways = (7* 6* 5* 4* 3* 2* 1)/(4* 3* 2* 1 * 3* 2* 1 ) =(5040)/(144) = 35`

Therefore, there are 35 paths we can take to walk from A to B via a 7 unit path while staying on the grid.