A cricket team has $15$ members, of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ drawn at random, then the chance of obtaining an eleven containing at least $3$ bowlers is

In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy $10$ ticket.

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

In a lottery there were $90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$ is

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -