A committee consists of $9$ experts taken from three institutions $A, B$ and $C$, of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign, then the probability that they belong to different institutions is

If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

$n$ 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

Each of the persons $\mathrm{A}$ and $\mathrm{B}$ independently tosses three fair coins. The probability that both of them get the same number of heads is :

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r_1, r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $\omega^{I_1}+\omega^{\mathrm{I}_2}+\omega^{\mathrm{I}_3}=0$ is