$A$ bag contains $3$ red,$4$ white,and $5$ black balls. Three balls are drawn at random. The probability that they are of different colours is

Three numbers are chosen from $1$ to $30$. The probability that they are not three consecutive numbers is

From a group of $10$ men and $5$ women,a four-member committee is to be formed such that it must contain at least one woman. The probability that the committee has more women than men is:

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

Nine balls are drawn simultaneously from a bag containing $5$ white and $7$ black balls. The probability of drawing $3$ white and $6$ black balls 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