$n$ 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

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many $3$-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?