$n$ cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is
$\frac{2}{n}$
$\frac{1}{n}$
$\frac{2}{{(n - 1)\,!}}$
None of these
There are $n$ different objects $1, 2, 3,......n$ distributed at random in $n$ places marked $1, 2, 3, ......n$. The probability that at least three of the objects occupy places corresponding to their number is
In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is
A committee of two persons is selected from two men and two women. What is the probability that the committee will have two men ?
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
If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :