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

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?

If $4$ cards are drawn one by one from a deck of $52$ cards,what is the probability that each card belongs to a different suit?

If two sections of strengths $30$ and $45$ are formed from $75$ students who are admitted in a school,then the probability that two particular students are always together in the same section is

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

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