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)
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)
- A
$\frac{{^{18}{C_2}}}{{^{22}{C_2}}}$
- B
$\frac{{^{20}{C_2}{.^{18}}{C_1}{.^{17}}{C_1}{{.3}^{16}}}}{{{3^{20}}}}$
- C
$\frac{{^{20}{C_2}}}{{{3^2}}}$
- D
$\frac{{{3^{20\,}} - \,{{13.2}^{20}}\, + \,\,43}}{{{3^{20}}}}$
Similar Questions
A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-
A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?
A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is
A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is
A drawer contains $5$ brown socks and $4$ blue socks well mixed. A man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match
A drawer contains $5$ brown socks and $4$ blue socks well mixed. A man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match
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 :
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 :
- [JEE MAIN 2021]