$A$ mapping is selected at random from the set of all the mappings of the set $A = \{1, 2, ..., n\}$ into itself. The probability that the mapping selected is an injection is

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

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw a sum of $9$ with both dice will be awarded the prize. If $A$ throws first,then the probability that $B$ wins the game 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 $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

If $A_1, A_2, \ldots, A_{15}$ are the events of a random experiment, then which one of the following is true?

From a pack of $52$ playing cards,three cards are drawn simultaneously. The probability that these are one king,one queen,and one jack is: