Exam 7: Sets and Counting

Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch six movies selected at random from the list. ?? Name Revenue ( ( million) The Grudge \ 9.24 Ray \ 6.54 The Forgotten \ 6.01 Friday Night Lights \ 5.99 Cellular \ 5.85 Shall We Dance \ 5.82 The Village \ 5.58 AVP: Alien Vs. Predator \ 5.46 Catwoman \ 5.10 Sky Captain and the World of Tomorrow \ 5.09 a. How many sets of six movies are possible ? __________ sets b. Your best friends, the Lara twins, refuse to see "Shall We Dance" on the grounds that it is "for girliemen" and also insists that at least one of "Alien Vs. Predator" or "Sky Captain" be among the movies selected. How many of the possible groups of six will satisfy the twins ? __________ groups c. Comparing the answers in parts (a) and (b), would you say the Lara twins are more likely than not to be satisfied with your random selection ? __________ (yes or no )

How many possible calendars are there that have February 11 falling on a Monday, or Tuesday ?

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 5 digits ?

In December 2001 a search using the Web search engine Google^TM for "Costenoble" yielded 10,000 Web sites containing that word. A search for "Waner" yielded 67,000 sites. A search for sites containing both words yielded 4,393 sites. How many Web sites contained either "Costenoble" or "Waner" or both ?

You would like to see either a Drama movie, or one that is based on a Comic book character but does not feature robots. Which set of movies are you interested in seeing Please answer in set notation.

Let $A = \{ \mathrm { H } , \mathrm { T } \}$ be the set of outcomes when a coin is tossed. ​ List the set of all outcomes of tossing a coin two times.

The number of ordered lists of 7 different items, chosen 4 at a time is 840.

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ .

Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible ?

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes ? __________ handshakes

Professor Tough's final examination has 13 true-false questions followed by 5 multiple-choice questions. In each of the multiple choice questions you must select the correct answer from a list of 5. How many answer sheets are possible __________ sheets

Let S be the set of outcomes when two distinguishable dice are rolled, let F be the subset of outcomes in which at least one die shows an odd number. List the elements of F'.

Use the given information to complete the solution of the partially solved Venn diagram. $n ( A ) = 23$ , $n ( B ) = 15$ , $n ( C ) = 25$ , and $n ( S ) = 53$

Let $A = \{ \text { June, Justine, Sally, Molly, Jello, Rachel } \}$ Find the set $A \cap \varnothing$ .

Let ​ $A = \{ \text { Janet, Justine, Sally, Jolly, Jello, Joan } \}$ ​ Find the set $A \cap \varnothing$ . ​ $A \cap \varnothing =$ __________

A test requires that you answer either Part A or Part B. Part A consists of 21 true/false questions and part B consists of 9 multiple choice questions with one correct answer out of 5. How many different completed answer sheets are possible

Let $A = \{ \mathrm { H } , \mathrm { T } \}$ be the set of outcomes when a coin is tossed. List the set of all outcomes of tossing a coin two times.

Of the 5,400 students at medium Suburban College, 60 play collegiate soccer, 56 play collegiate lacrosse, and 95 play collegiate football. Only 4 play both collegiate soccer and lacrosse, 5 play collegiate soccer and football, and 25 play collegiate lacrosse and football. No students play all three sports. ​ Complete the following sentence. Round your answer to the nearest percent. ​ __________% of the college soccer players also play one of the other two sports at the collegiate level.

Let ​ A =\{ June, Jill, Sally, Jolly \} B =\{ Jill, Jolly, Jennifer \} C =\{ Ruth, Jill, Jolly \} ​ Find the set $C \cap B$ .

In December 2001 a search using the Web search engine Google ^TM for "Costenoble" yielded 11,000 Web sites containing that word. A search for "Waner" yielded 67,000 sites. A search for sites containing both words yielded 4,161 sites. How many Web sites contained either "Costenoble" or "Waner" or both ? The number of Web sites is __________.