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 ....

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?

$A$ dice is rolled three times. The probability of getting a larger number than the previous number each time is:

Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as $4$,and the person who gets this result first is declared as the winner. If $A$ starts the game,then the probability that $B$ wins the game is:

An urn contains nine balls of which three are red,four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.$ $A$ mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is