If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is
$12/49$
$6/49$
$9/49$
$15/49$
Two numbers $x$ $\&$ $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, ......, 1000\}$. Then the probability that $|x^4 - y^4|$ is divisible by $5$, is -
From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is
There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is
Three distinct numbers are selected from first $100$ natural numbers. The probability that all the three numbers are divisible by $2$ and $3$ is
In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy $10$ ticket.