Worksheet: The Basic Principle of Counting

Worksheet for Section 1.1–1.2The Basic Principle of CountingV63.0233, Theory of ProbabilityJune 29, 20091.At Pat’s Cheese Steaks in Philadelphia you can order a cheesesteak with or without saut´eedonions, and with your choice of provolone cheese, american cheese, or Cheez Whiz. (In the nativeparlance, a typical order sounds like “Whiz, wit’.”)How many different ways can you order your cheesesteak?2.Consider flipping a coin two times.(a) How many possible sequences of flips are there?(b) What percentage of the possibilities have two heads?(c) What percentage of the possibilities have an even number of heads?3.Consider flipping a coin four times.(a) How many possible sequences of flips are there?(b) What percentage of the possibilities have two heads?(c) What percentage of the possibilities have an even number of heads?4.In Indiana from 1963 through 2008, license plates were coded by the following scheme:• The number of the county the licensee resides in, arranged alphabetically from 1 to 93• a letter• a four-digit numberAn example might be “82a5713”. How many license plates may be printed according to thisscheme?5.Since 2008, Indiana license plates are coded by a three-digit number and from one to threeletters. How many license plates are possible in this scheme?6.The current format of area codes is three digits, where• The first digit can be any number but 0 or 1• The second digit can be any number between 0 and 8• The third digit can be any number at all, except that the last two digits cannot both be 11So 781 is a valid area code but not 187 or 411. How many possible area codes are there?7.In the days of rotary telephones, area codes were restricted to a different format:• The first digit could be any number but 0 or 1• The second digit had to be 0 or 1• The third digit could be from 1 to 9 if the second digit was 0, and from 2 to 9 if the seconddigit was 1.So 617 is a valid area code, but not 781 (back then), nor 411. This was to make dialing easier andto give the most populous areas the smallest number of total clicks. How many possible area codeswere there then?8.Packing his belongings to go to college, a student has to decide what to do about his CDcollection. In how many different ways can he take a long at least one of his 10 favorite CDs?2