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

Ten students are seated at random in a row. The probability that two particular students are not seated side by side 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

Two marbles are drawn in succession from a box containing $10$ red, $30$ white, $20$ blue and $15$ orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then the probability that $2$ are white and $1$ is red, is

Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is