$n$ 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

Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels, then what is the probability that atleast $2$ of them goes in hotel $x$, atleast $1$ in hotel $y$ and atleast $1$ in hotel $z$ ? (each hotel has capacity for more than $20$ guests)

A bag contains $3$ red, $7$ white and $4$ black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

If four persons are chosen at random from a group of $3$ men, $2$ women and $4 $ children. Then the probability that exactly two of them are children, is

If out of $20$ consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is

A box contains $25$ tickets numbered $1, 2, ....... 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is