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# Telephone numbers in the US start with a 3 digit area code followed by a 7 digit local number.

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Telephone numbers in the US start with a 3 digit area code followed by a 7 digit local number. Assume that any number (0­9) is possible for each digit.(5 points each)a) How many different area codes are possible?b) What is the probability that an area code starts with a 5?c) For a given area code, how many different local numbers are possible?d) How many different complete telephone numbers are possible? 2. How many different batting orders are possible for a 9 player baseball team? 3. John has a standard deck of cards. After shuffling them, he deals you a 5 card hand.What is the probability that your hand contains the following 5 cards: Ace of Hearts, Jack of Spades, 3 of Clubs, 5 of Hearts and 7 of Diamonds? Note: the order that the cards are dealt is not important here.4. On the price is right, there is a display of 5 products with prices associated with each. For each product, the player has to guess whether or not the price is too high or too low. Assuming that Jenny knows nothing about the prices of the products displayed (that is, there is an equal probability of the price being too high or too low), what is the probability that she gets all 5 guesses correct?5. A favorite game on the Price is Right is called “Plinko”. A single ball is dropped at the top and hits a series of pegs as it falls. At each peg, the ball can go in one of two ways (right or left) with equal probability. Consider the following (modified) “Plinko” board. How many different paths are possible?6. The senate consists of 2 representatives from each US State for a total of 100 people.A 5 person committee is formed to attack a particular issue. a. How many different 5 person committees are possible?b. If the senate is comprised of 20 females and 80 males and the committee must contain exactly 2 females, then how many different 5 person committees are possible?© 2014 Trustees of Boston University. Materials contained within this course are subject to copyright protection.7. A bag contains a red marble, a blue marble and a yellow marble. A marble is selected at random 3 times with replacement. How many events will form a full group of events? Also, list all of these events in which the first draw results in a red marble being selected.8. A cube has all of its sides painted in blue and then is cut into 1000 cubes of the samesize. All cubes are placed in an urn and are thoroughly mixed, so that the probability of being randomly picked from the urn is the same for all cubes. What is the probability that a randomly picked cube has at least one of its sides painted blue?9. You roll a fair 6­sided die 8 times. What is the probability that you will roll at least four “4’s”?Complementary problem (worth up to 3 extra credit points)10. There are twelve raffle tickets, three of which are winners. Find the probability that in a sample of 5 tickets there will be no more than one winning ticket.

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