Consider the 6 × 6 square in the figure. Let ${\mathrm{A}}_1,{\mathrm{A}}_2,\dots ,{\mathrm{A}}_{49}$ be the points of intersections (dots in the picture) in some order. We say that ${\mathrm{A}}_{\mathrm{i}}$ and ${\mathrm{A}}_{\mathrm{j}}$ are friends if they are adjacent along a row or along a column. Assume that each point ${\mathrm{A}}_{\mathrm{i}}$ has an equal chance of being chosen.