Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1,2,3,4,5$ and $6$ are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$ is

If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters are posted to exactly two addresses is:

A committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in committee, is

A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is

Mr. A has six children and atleast one child is a girl, then probability that Mr. A has $3$ boys and $3$ girls, is 

Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1,2,3,4......15\}.$ The probability that point $(x,y)$ lies on a line through $(0,0)$ having slope $\frac{2}{3}$ is