Out of $13$ applicants for a job,$5$ are women and $8$ are men. Two persons are to be selected for the job. What is the probability that at least one woman is selected?

$A$ box contains $25$ tickets numbered $1, 2, \dots, 25$. If two tickets are drawn at random,then the probability that the product of their numbers is even is:

$A$ bag contains $6$ red,$2$ white and $8$ blue balls. Three balls are drawn at random from the bag. Match the items of List-$I$ with those of List-$II$.

$A$. Probability that none of the balls is white	$I$. $\frac{1}{70}$
$B$. Probability of getting $2$ white and $1$ blue ball	$II$. $\frac{6}{35}$
$C$. Probability of getting $2$ blue and $1$ white ball	$III$. $\frac{13}{20}$
$D$. Probability of getting $1$ red,$1$ white and $1$ blue ball	$IV$. $\frac{1}{10}$

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

The probability that three cards drawn from a pack of $52$ cards are all red is

$4$ boys and $2$ girls occupy seats in a row at random. The probability that the two girls occupy seats side by side is: