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

A card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a square is

Five numbers $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ are randomly selected from the numbers $1,2,3, \ldots \ldots, 18$ and are arranged in the increasing order $\left( x _{1}< x _{2}< x _{3}< x _{4}< x _{5}\right)$. The probability that $x_{2}=7$ and $x_{4}=11$ is

There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne probability that all get admission in different colleges can be expressed as $\frac {a}{b}$ where $a$ and $b$ are co-prime numbers then the value of $a + b$ is

In a box there are $2$ red, $3$ black and $4$ white balls. Out of these three balls are drawn together. The probability of these being of same colour is