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
$\frac{{n\,!}}{{(n - m)\,!\,{m^n}}}$
$\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}$
$\frac{{m\,!}}{{(n - m)\,!\,{n^m}}}$
$\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}$
Six points are there on a circle . Two triangles are drawn with no vertex common. What is the probability that none of the sides of the triangles intersect
A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is at least one pair is equal to
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?
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
One of the two events must occur. If the chance of one is $\frac{{2}}{{3}}$ of the other, then odds in favour of the other are