If a $5$-digit number is chosen at random,what is the probability that all digits are distinct,odd digits occupy odd places,and even digits occupy even places?

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 ————

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .

If three cards are drawn randomly from a pack of $52$ playing cards, then the probability of getting exactly one spade card, exactly one king, and exactly one card having a prime number is

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:

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