JEE Advanced 2023 — Paper 2 — Question 38

Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \ldots . ., A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{\mathrm{i}}$ and $A_{\mathrm{j}}$ are friends if they are adjacent along a row or along a column. Assume that each point $A_{\mathrm{i}}$ has an equal chance of being chosen.

Two distinct points are chosen randomly out of the points $\mathrm{A}_{1}, \mathrm{~A}_{2}, \ldots . ., \mathrm{A}_{49}$. Let $p$ be the probability that they are friends. Then the value of $7 p$ is