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 :
$22{\left( {\frac{1}{3}} \right)^{11}}$
$\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}$
$55{\left( {\frac{2}{3}} \right)^{10}}$
$220{\left( {\frac{1}{3}} \right)^{12}}$
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :
If a leap year is selected at random, what is the change that it will contain $53$ Tuesdays ?
Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.\,$ A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is
A bag contains $4$ white, $5$ red and $6$ black balls. If two balls are drawn at random, then the probability that one of them is white is
A bag contains $20$ coins. If the probability that bag contains exactly $4$ biased coin is $1/3$ and that of exactly $5$ biased coin is $2/3$,then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is