If three integers are selected at random from the first $20$ integers,what is the probability that their product is even?

Two different families $A$ and $B$ are blessed with an equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of family $B$ is $\frac{1}{12}$,then the number of children in each family is?

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 ....

If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is

If $6$ girls and $5$ boys are sitting in a row,what is the probability that no two boys sit together?

$A$ sample of $4$ items is drawn at random without replacement from a lot of $10$ items containing $3$ defective items. If $X$ denotes the number of defective items in the sample,then $P(0 < X < 3)$ is equal to: