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

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :

A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q- p$ is equal to

A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is

If six students, including two particular students $A$ and $B,$ stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is