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

A committee of five is to be chosen from a group of $9$ people. The probability that a certain married couple will either serve together or not at all, is

The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, 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

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

Out of $30$ consecutive numbers, $2$ are chosen at random. The probability that their sum is odd, is