CHAPTER 1. SETS AND COUNTING Review Exercises 1 . A survey asked 200 business owners about their leisure activities . It was found that 90 read , 60

How is the answer to #1 42? I got 60. What am I doing wrong? please explain

CHAPTER 1. SETS AND COUNTINGReview Exercises1 . A survey asked 200 business owners about their leisure activities . It was found that 90read , 60 jog , 40 garden , 12 read and jog , 16 read and garden , 10 jog and garden , and6 do all three activities . How many of the surveyed business owners do not do any ofthese three activities ?!Idea : Draw a Venn Diagram . What region is being described by the question ? Whatis the complement of this region ?!2 . The host of a party wants to order 3 salads , 4 hot dishes , and 2 desserts from a cateringcompany . The company offers 7 different salads , 6 hot dishes , and 5 desserts . Howmany ways can the host of the party select which items to order ?"Idea : Use the Multiplication Principle . How many ways are there to decide which3 of the 7 salads to order ? Answer a similar question for the hot dishes and for thedesserts . The Multiplication Principle says what to do with these three numbers .3 . In how many distinguishable ways can the 9 letters in { , N . I . E, R, I , A, I , N bearranged in a row such that the two Is are adjacent and the two I's are adjacent ?!Idea : Use the " glue" method . Treat NN as one object , and do the same for IT . Howmany objects are there now ? Are any identical ?4 . Calum wants to make a linear arrangement of & cards taken from a standard deck of52 cards . He wants each card to have a different rank and does not want any card tohave the same suit as the cards directly next to it . How many ways can Calum makesuch an arrangement ?"Idea : How many options are there for the & ranks that Calum will decide to use ? Howmany orders for these ranks are possible ? Once the rank of each position has beendetermined , select the suit for each position , one at a time , making sure adjacent cardsget different suits .5 . A small design company gives each of its products a code that consists of two lettersfollowed by four digits . How many different codes can be formed such that the lettersare taken from [A , B , C, D; and may include repetition , and the four digits are takenfrom ( 1 , 2 , 3 , 4 , 5 , 6 , 7, 8, 9} and must be all different and arranged in decreasing order ?about the second ? Flow