If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :
$22{\left( {\frac{1}{3}} \right)^{11}}$
$\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}$
$55{\left( {\frac{2}{3}} \right)^{10}}$
$220{\left( {\frac{1}{3}} \right)^{12}}$
A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles. $5$ marbles are drawn from the box, what is the probability that atleast one will be green?
A bag contains $5$ white, $7$ black and $4$ red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white, is
In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.
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)
Three distinct numbers are selected from first $100$ natural numbers. The probability that all the three numbers are divisible by $2$ and $3$ is