A board has 16 squares (4 4 grid).

Question

A board has 16 squares (4	imes 4 grid). Out of these, two squares are chosen at random. The probability that they have no side in common is:

Accepted Answer

Total ways to select 2 squares $={}^{16}C_2=120$.

Number of adjacent (side-sharing) pairs in a 4\times 4 grid $=24$.

$$P(\text{no side common}) = 1-\frac{24}{120}=\frac45$$

Solutions · 1