A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then the probability that $2$ are white and $1$ is red, is

In an examination, there are $10$ true-false type questions. Out of $10$ , a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k }{4^{10}}$, then $k$ is equal to

If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -

A bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected randomwise, the probability that it is a black or red ball is

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

A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then