If $12$ identical balls are to be placed randomly in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is
$\frac{4}{{19}}$
$\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}$
$\frac{{\left( {428} \right){}^{12}{C_3}}}{{{3^{11}}}}$
$\frac{5}{{19}}$
From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is
Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is
If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are
Two marbles are drawn in succession from a box containing $10$ red, $30$ white, $20$ blue and $15$ orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is
Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is