a) Provide a written description of the complement of each of the given events below: i. When a couple has three children, at least one of them is a girl. ii. When 12 apples are tested for freshness, all of them pass the test. iii. In a Statistics class, all students receive a grade A. iv. When five missiles are fired, at least one of them strikes its target. v. When a coin is flipped, a head is obtained.

b) A deck of cards contains 10 red cards numbered 1 to 10 and 10 black cards numbered 1 to 10. How many ways are there of arranging the 20 cards in a row? Suppose we draw the cards at random and lay them in a row. What is the probability that red and black cards alternate?

c) A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women alternate?