If $4$ boys and $3$ girls are standing in a row for an interview,what is the probability that they stand in alternating positions?

$A$ board has $16$ squares arranged in a $4 \times 4$ grid. Out of these $16$ squares,two squares are chosen at random. The probability that they have no side in common 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

$A$ bag contains $4$ red, $3$ white, and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.

List-$I$	List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball	$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball	$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball	$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

Out of $30$ consecutive numbers,$2$ are chosen at random. The probability that their sum is odd,is

$A$ seven-digit number is formed using the digits $3, 3, 4, 4, 4, 5, 5$. The probability that the number so formed is divisible by $2$ is ..... .