15 students join a summer course.Every day 3 students are on duty after school to clean the class rooms.After the course,it was found that every pair of students has been on duty exactly once.How many days does the course last for(a)35(b)45(c)(105(d)none of these

• 35 days.
  
  No of combinations of 3 students from 15 students = 15!/(12!*3!) = 15*14*13/6= 35*13
  
  but here each pair has worked with other 13 persons once.
  As per given condition , each pair worked together only once.
  so possible combinations = no of days of course = 35*13/13= 35
• 12 years agoHelpfull: Yes(5) No(9)