In a certain lottery,$10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy $2$ tickets?

$A$ box contains $5$ blue and $4$ white chalks. If two chalks are chosen at random,what is the probability that both chalks are of the same color?

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

If the letters of the word "$UNIVERSITY$" are arranged at random,what is the probability that both '$I$'s do not come together (in $/5$)?

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

Five persons enter a lift cabin in the cellar of a $7$-floor building (excluding the cellar). If each of them independently and with equal probability can leave the cabin at any floor out of the $7$ floors (beginning with the first),then the probability that all $5$ persons leave the cabin at different floors is: