Question

If nine squares are chosen at random on a chess board, The probability that they form a square of size $3\times 3$ is $=\frac{6k}{{{}^{64}C}_9}$.Find $k$

Answer 1

$S:$ Number of ways of selecting $9$ square from $64$ is ${}^{64}{C}_9$

$E:$ Number of ways of $3\times 3$ square $=36$

$\therefore$ Required probability$=\frac{364}{{}^{64}{C}_9}$

$\Rightarrow k=6$