$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is

A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is  shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is

If four persons are chosen at random from a group of $3$ men, $2$ women and $4 $ children. Then the probability that exactly two of them are children, is

Let $S$ be the sample space of all five digit numbers.If $p$ is the probability that a randomly selected number from $S$, is a multiple of $7$ but not divisible by $5$ , then $9\,p$ is equal to.