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

Two numbers are selected randomly from the set $S = \{ 1,\,2,\,3,\,4,\,5,\,6\} $ without replacement one by one. The probability that minimum of the two numbers is less than $4$ is

If $12$ identical balls are to be placed randomly in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is

In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)

A bag contains $3$ white and $7$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

$n$ 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