A box contains 24 light bulbs, of which two are defective. If a person selects 10 bulbs at random, without replacement, what is the probability that both defective bulbs will be selected?

  

Suppose that four guests check their hats when they arrive at a restaurant, and that these hats are returned to them in a random order when they leave. Determine the probability that no guest will receive the proper hat.

 Suppose that n letters are placed at random in n envelopes, and let qn denote the probability that no letter is placed in the correct envelope. For which of the following four values of n is qn largest : n = 10, n = 21, n = 53 or n = 300?

 Each year starts on one of the seven days (Sunday, through Saturday). Each year is either a leap year (i.e. it includes February 29) or not. How many different calendars are possible for a year?