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

Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels, then what is the probability that atleast $2$ of them goes in hotel $x$, atleast $1$ in hotel $y$ and atleast $1$ in hotel $z$ ? (each hotel has capacity for more than $20$ guests)

Among $15$ players, $8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers

Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is

An urn contains $6$ white and $9$ black balls. Two successive draws of $4$ balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is:

From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is