Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to daughters of $A$ is $1/20$. The number of daughters each of them have 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

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 $5$ 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

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

If two different numbers are taken from the set $\left\{ {0,1,2,3, \ldots ,10} \right\}$, then the probability that their sum as well as absolute difference are both multiple of $4$, is