Quiz 2 car car vrr Solution. First, let's park the SUVs. The number of ways to do this is equal to the number of ways to select 20 books off of a shelf such that adjacent books are not selected-a problem of a type you' ve seen before. The answer is(4). Now the 10 cars can be parked in the remaining g spaces in (10)ways. So the total number of parking possibilities is (e)A mobile is a hanging structure built from seven horizontal rods (indicated with solid lines), seven vertical strings(indicated with dotted lines), and eight toys (indi cated with the letters A-h B C D E Many different toy arrangements can be obtained by twisting the strings. For ex ample, twisting the string marked with the arrow would swap toys A and B Twisting the string marked with the +arrow would reverse the order of toys e, F, G, and H On the other hand, no combination of twists swaps only toys b and C. Two mobiles are different if one can not be obtained from the other by twisting strings. How many different mobiles are possible? Solution. There are 8! different sequences of toys. Each mobile can be configured in 2 different ways, by twisting or not twisting the 7 upper strings. Thus, there is a 2-to-1 mapping from sequences to mobiles. By the Division Rule, the number of different mobiles is 8! /2=315� � � � � � � � Quiz 2 9 S c c c S c S c c c c S c c U a a a U a U a a a a U a a V r r r V r V r r r r V r r Solution. First, let’s park the SUVs. The number of ways to do this is equal to the number of ways to select 20 books off of a shelf such that adjacent books are not selected— a problem of a type you’ve seen before. The answer is 17 . Now the 10 4 cars can be parked in the 16 remaining spaces in 16 ways. So the total number of 10 parking possibilities is: 17 16 4 · 10 (e) A mobile is a hanging structure built from seven horizontal rods (indicated with solid lines), seven vertical strings (indicated with dotted lines), and eight toys (indi￾cated with the letters A­H).   - A B C D E F G H Many different toy arrangements can be obtained by twisting the strings. For ex￾ample, twisting the string marked with the → arrow would swap toys A and B. Twisting the string marked with the ← arrow would reverse the order of toys E, F, G, and H. On the other hand, no combination of twists swaps only toys B and C. Two mobiles are different if one can not be obtained from the other by twisting strings. How many different mobiles are possible? Solution. There are 8! different sequences of toys. Each mobile can be configured in 27 different ways, by twisting or not twisting the 7 upper strings. Thus, there is a 27­to­1 mapping from sequences to mobiles. By the Division Rule, the number of different mobiles is 8!/27 = 315.