$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red 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:

If $4$ boys and $3$ girls are standing in a row for an interview,what is the probability that they stand in alternating positions?

$A$ total of $13$ people,consisting of $5$ women and $8$ men,have applied for a job. If $2$ people are to be selected from these $13$ people,what is the probability that at least one woman is selected?

$A$ four-digit number is to be formed using the digits $1, 2, 3, 4, 5, 6, 7$ (no digit is repeated). What is the probability that the number formed is $> 4000$?

$A$ $5$-digit number is formed using the digits $1, 2, 3, 4, 5, 6,$ and $8$. What is the probability that the number has even digits at both ends?