All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is 

From a group of $7$ men and $4$ ladies a committee of $6$ persons is formed, then the probability that the committee contains $2$ ladies is

Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

A box contains $25$ tickets numbered $1, 2, ....... 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is

$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression

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