Question

A grid is set up as shown using 5 horizontal and 6 vertical lines. What are the no. of ways one can go from point P to point Q walking along the grids but not moving upwards or left or retracing a grid?

• A. 21
• B. 35
• C. 56
• D. None of these

Answer 1

The correct option is D None of these

If someone is going from P to Q. He has to travel 4 times vertically and 5 times horizontally. Ultimately, we are arranging 4 - V's and 5 - H's .

Number of ways to arrange 4 - V's and 5 - H's = $\frac{9!}{(4!\times 5!)}{=}^9{C}_4{=}^9{C}_5$

Or, There are 4 rows and 5 columns. Using the one-zero method, number of paths will be ${}^9{C}_4$ = 126 ways