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 $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to

Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X)$ with replacement,then the probability that $A$ and $B$ have an equal number of elements is:

$A$ sample of $4$ items is drawn at random without replacement from a lot of $10$ items containing $3$ defective items. If $X$ denotes the number of defective items in the sample,then $P(0 < X < 3)$ is equal to:

If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is

$A$ box contains $2$ black,$4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box,another ball is drawn at random and kept aside the first. This process is repeated until all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black,$4$ white and $3$ red is