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

• It is given in the prob., that every pair of students has been on duty exactly once. This suggests that the number of days the course lasts for is equal to the number of ways in which 2 students from 15 students can be selected.
  Now, it is well-known fact that the number of ways in which 2 students from 15 students can be selected = (15C2) = [15!/{(13!)*(2!)}] = 7*15 = 105.
  
  So, evidently, the course lasts for 105 days .
  
  So, the correct answer is OPTION c) 105 .
  
  Thanks to All..:-):-)
• 11 years agoHelpfull: Yes(50) No(20)
• no of pairs=15C2=15!/(2!13!)=7*15
  no of pairs cleaning each day=3C2=3
  no of days=7*15/3=35
• 11 years agoHelpfull: Yes(39) No(8)
• sorry it will be
  15c2=105(ans)
• 11 years agoHelpfull: Yes(13) No(11)
• HYE ITS GIVEN THAT E STUDENTS ARE ON DUTY..... HOW U GUYS TOOK 15C2???? its 15C3 naaaaa????
• 11 years agoHelpfull: Yes(12) No(11)
• @sdeep bhattacharya..the idea of taking 2 students at a time is correct..bt the q says 3 students form a pair...so the no days the course shud last shud be equal to the no of ways in which 3 students can b selectd out of 15 i.e. 15C3..
• 11 years agoHelpfull: Yes(10) No(3)
• dekho bhai garmi ki chuttiya 45 din ki hoti hai to ans will be 45
• 11 years agoHelpfull: Yes(10) No(10)
• the answer to this que. is a) 35, since total 105 pairs are present (14+13+12+11+..........+1=105) and each day 3 pairs are present (since 3 students form 3 pairs) hence 105 pairs will be present in 105/3 Days= 35 DAYs
• 11 years agoHelpfull: Yes(7) No(0)
• solution is not clear, all r wrong.
  ans would be "none of these".
• 11 years agoHelpfull: Yes(6) No(1)
• ans would be 15c2=105.
  bcoz there will be only 105 pairs will appear for work exactly once.
  logic is that remaing one out of three may be any student.
  so two student r selected from combination of 15c2 at a time.
• 11 years agoHelpfull: Yes(4) No(2)
• well,,i think it will be the combination of 15 students taking 2 at a time...
  15C2=105
  c)105
• 11 years agoHelpfull: Yes(3) No(7)
• @P M ANOOP SABIR
  your answer seems to be correct but y not the answer is 105
• 11 years agoHelpfull: Yes(3) No(1)
• 15+12+9+6+3=45
  b)45(ans)
• 11 years agoHelpfull: Yes(2) No(24)
• your answer seems to be correct but y not the answer is 105
• 11 years agoHelpfull: Yes(2) No(2)
• it says three students not 2.......so the ans shd be 15c3
  i.e. none of these d)
• 9 years agoHelpfull: Yes(0) No(0)
• correct ans : 35
  15C2 =105
  
  and a group of 3 persons consists of 3 pairs
  
  so 105/3=35
• 9 years agoHelpfull: Yes(0) No(0)