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

In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)

Two numbers are selected at random from $1, 2, 3 ……100$ and are multiplied, then the probability correct to two places of decimals that the product thus obtained is divisible by $3$, 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

A bag contains tickets numbered from $1$ to $20$. Two tickets are drawn. The probability that both the numbers are prime, is