A dice is rolled three times, find the probability of getting a larger number than the previous number each time ?

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is

Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

A bag contains, $7$ different Black balls .and $10$ different Red balls, if one by one ball are randomely drawn untill all black balls are not drawn, then probability that this process is completed in $12 ^{th}$ draw, is equal to 

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is

Five numbers $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ are randomly selected from the numbers $1,2,3, \ldots \ldots, 18$ and are arranged in the increasing order $\left( x _{1}< x _{2}< x _{3}< x _{4}< x _{5}\right)$. The probability that $x_{2}=7$ and $x_{4}=11$ is