Question

Four small squares on a chess board are selected at random. The probability that they form a square of the size $2\times 2$ is $\frac{k}{90768}$. Find the value of $k$.

Answer 1

Total number of ways of selecting $4$ squares is $64$.
Number of ways of selecting square of size $2\times 2$
$=7\times 7=49$
$\therefore$ Required probability
$=\frac{49}{{}^{64}{C}_4}=\frac{7}{90768}$