The probability of getting a sum of $16$ in a single throw with three dice 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 $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

From a well-shuffled deck of $52$ cards,$13$ cards are selected at random. The probability that the selected $13$ cards contain exactly $4$ kings is ....

From $3n$ consecutive integers,three integers are selected at random. The probability that their sum is divisible by $3$ is

$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

Two numbers $x$ and $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $|x^4 - y^4|$ is divisible by $5$ is -