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

Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of spade is

Three distinct numbers are selected from first $100$ natural numbers. The probability that all the three numbers are divisible by $2$ and $3$ is

From a class of $12$ girls and $18$ boys, two students are chosen randomly. What is the probability that both of them are girls

Mr. $A$ has six children and atleast one child is a girl, then probability that Mr. $A$ has $3$ boys and $3$ girls, is -
 

A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is