Twenty tickets are marked with the numbers $1, 2, \dots, 20$. If three tickets are drawn at random,what is the probability that the tickets marked $7$ and $11$ are among them?

There are four machines and it is known that exactly two of them are faulty. They are tested,one by one,in a random order until both the faulty machines are identified. Then the probability that only two tests are needed is

Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

$A$ flashlight has $10$ batteries,out of which $4$ are dead. If $3$ batteries are selected without replacement and tested,then the probability that all $3$ are dead is:

$A$ bag contains $5$ blue and an unknown number $x$ of red balls. Two balls are drawn at random. If the probability of both of them being blue is $\frac{5}{14}$,then the value of $x$ is equal to

Five persons enter a lift cabin in the cellar of a $7$-floor building (excluding the cellar). If each of them independently and with equal probability can leave the cabin at any floor out of the $7$ floors (beginning with the first),then the probability that all $5$ persons leave the cabin at different floors is: