In a game of cards,what is the probability that a specific player holds all $4$ kings in a hand of $13$ cards?

Two cards are drawn at random from a standard pack of $52$ cards. The probability that the draw consists of exactly one face card and exactly one ace card is

Ten persons with badges numbered $1$ to $10$ are in a room. If three of them are asked to leave the room, then the probability that the person with the smallest badge number among the three who left is $5$, 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 $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

Three integers are chosen at random from the first $20$ integers. The probability that their product is even,is

Out of $13$ applicants for a job,there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is