A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

An ordinary cube has four blank faces, one face marked $2$ another marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws, is

A committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in committee, is

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Probability that  the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ is equal to

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