Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$,where $p$ and $q$ are co-prime,then $q-p$ is equal to

$A$ bag contains $8$ red and $7$ black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

Two cards are drawn at random from a well-shuffled pack of $52$ cards. Find the probability that one card is a prime number and the other is a multiple of $5$.

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then,the probability that balls of both colours are drawn is

Out of $13$ applicants for a job,there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to