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 

A bag contains $3$ red, $7$ white and $4$ black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

Probability that  the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ 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

Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random, the probability that $A$ and $B$ have the same number of elements, is

Two dice are thrown  $5$ times, and each time the sum of the numbers obtained being  $5$ is considered a success. If the probability of having at least $4$ successes is $\frac{\mathrm{k}}{3^{11}}$, then $\mathrm{k}$ is equal to