Question

Four different letters are distributed at random into 5 mailboxes by choosing one of the five...

Four different letters are distributed at random into 5 mailboxes by choosing one of the five mailboxes at random for each of the letters.

a. Give a possible sample space for this problem. How many points are in the sample space?

b. Find the probability that no mailbox contains more than one letter.

c. Find the probability that the first two mailboxes are not both empty.

Please include explanations throughout your solution.

d. Let a random variable X be defined as X = "number of empty mailboxes". Find P(X = j) for j = 5,4, and j = 3.

Math   Statistics-And-Probability   
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