Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is

The probability that a randomly chosen $5-digit$ number is made from exactly two digits is

In a lottery $50$ tickets are sold in which $14$ are of prize. A man bought $2$ tickets, then the probability that the man win the prize, is

If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

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

A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is: