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?

If $4$ letters are selected at random from the letters of the word $PROBABILITY$, then the probability of getting a combination of letters in which at least one letter is repeated is

$A$ bag contains $4$ red and $4$ blue balls. Four balls are drawn one by one from the bag. Find the probability that the drawn balls are of alternating colors.

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:

If a coin is tossed $n$ times,then the probability that the head comes up an odd number of times is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains exactly $3$ Kings.