New public school have a circular layout. The school has teachers specializing in various subjects. All classroom of the school are equally spaced apart and located along its perimeter. Each Teacher needs four classes in day. There is strange rule.the first and last class has to be in the same class room. The other two classes have to be at two other distinct class rooms. Answer the following
a:) Bharti is a history teacher.in addition to above rule of the school she teaches exactly one pair of successive classes in adjacent classrooms.how many distinct trips to classes rooms are possible for Bharti if there are 12 classroom in school.

• Case 1 : Only first class and second class are held in adjacent class rooms
  
  First class and fourth class can be in any of the 12 classrooms (12 ways)
  Second class can be in any of the two adjacent class rooms of first class (2 ways)
  Third class room can be any of the 8 class rooms which are not adjacent to second class room or fourth class room (8 ways)
  
  Total distinct trips possible in this case are 12×2×8 = 192
  
  Case 2: Only second class and third class are in adjacent class rooms
  
  Second class can be in any of the 12 classrooms (12 ways)
  Third class can be in any of the the two adjacent class rooms (2 ways)
  First class and fourth class can be in any of the the 8 class rooms (which are not adjacent to second and third classes)
  
  Total distinct trips possible in this case are 12×2×8= 192
  
  Case 3: Only third class and fourth class are in adjacent class rooms
  
  Third class can be in any of the 12 classrooms (12 ways)
  Fourth and first class can be in any of the the two adjacent class rooms (2 ways)
  Second class can be in any of the the 8 class rooms (which are not adjacent to first and third classes)
  
  Total distinct trips possible in this case are 12×2×8= 192
  
  Required number of distinct trips to classes rooms = 192+192+192 = 576
• 8 years agoHelpfull: Yes(9) No(3)
• still its not clear to me :(
• 8 years agoHelpfull: Yes(5) No(1)