Question

Four small squares on a chess board are selected at random. the probability that they form a square of the size 2 X 2 is $\frac{a}{b}$, where HCF of a and b is 1, then $a+b=?$

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
$=\frac{49}{{}^{64}{C}_4}=\frac{7}{90768}$
Therefore $a+b=7+90768=90775$