An urn contains $6$ white and $9$ black balls. Two successive draws of $4$ balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is:

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :

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

In a box there are $2$ red, $3$ black and $4$ white balls. Out of these three balls are drawn together. The probability of these being of same colour 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

$n$ cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is