From a collection of eight cards numbered $1$ to $8$,if two cards are drawn at random,one after the other with replacement,then the probability that the product of the numbers that appear on the cards is a perfect square is

$A$ container contains nine balls: three red,four blue,and two green. If three balls are selected at random from the container without replacement,what is the probability that all three balls are of different colors?

The probability of forming a $12$-person committee from $4$ engineers,$2$ doctors,and $10$ professors containing at least $3$ engineers and at least $1$ doctor is:

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her is:

Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$.
Statement-$1$: The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{85}$.
Statement-$2$: If the four chosen numbers form an $A.P.$,then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then,the probability that balls of both colours are drawn is