Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions?

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:

From a well-shuffled pack of $52$ cards,two cards are drawn at random. The probability that both cards are kings is:

All the spades are taken out from a pack of cards. From these cards,cards are drawn one by one without replacement until the ace of spades comes. The probability that the ace of spades comes in the $4^{th}$ draw is

Two bolts,two nuts,and three needles are in a box. Two parts are chosen at random from the box. What is the probability that one is a bolt and one is a needle?

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