Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels, then what is the probability that atleast $2$ of them goes in hotel $x$, atleast $1$ in hotel $y$ and atleast $1$ in hotel $z$ ? (each hotel has capacity for more than $20$ guests)

Let $S=\{1,2,3,4,5,6\} .$ Then the probability that a randomly chosen onto function $\mathrm{g}$ from $\mathrm{S}$ to $\mathrm{S}$ satisfies $g(3)=2 g(1)$ is :

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

From a well shuffled pack of $52$ playing cards, cards are drawn one by one with replacement. Probability that $5^{th}$ card will be "king of hearts" is

In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)

There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is