$n$ 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

How many different signals can be generated using $5$ flags from $8$ flags of different colors?

$S_1, S_2, \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$,then the number of ways the speakers address is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. The number of words which have at least one letter repeated is

$A$ dictionary is printed consisting of $7$-lettered words only that can be made using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

The number of ways in which $3$ men and $3$ women can be arranged in a row of $6$ seats,such that the first and last seats must be filled by men is