In how many ways can seven different objects be divided among three persons so that either 1 or 2 of them do not get any object
1. 180
2. 381
3. 36
4. 84

• when 2 person does not get any object -
  all items go to 1 person hence 3 ways
  when 1 person does not get any object -
  A gets 1 object B gets 6 -7c1
  A gets 2 object B gets 5 -7c2
  A gets 3 object B gets 4 -7c3
  A gets 4 object B gets 3 -7c4
  A gets 5 object B gets 2 -7c5
  A gets 6 object B gets 1 -7c6
  =126
  now either A gets 0 or B gets 0 or C gets 0 object so,126*3=378 ways
  total ways=378+3=381 ways(ans).
  
• 9 years agoHelpfull: Yes(18) No(2)
• 1 of them do not get any object= remaining 2 of them took all the objects(there are 3 ways to do this) = 3*( 7C1*6C6 + 7C2*5C5 + 7C3*4C4 )=378
  
  now, 2 of them do not get any object= 1 of them took all the objects (again there are 3 ways to do this)=3*(7C7)=3
  
  so ans is =378 + 3 = 381
• 9 years agoHelpfull: Yes(10) No(1)
• when 1 person does not get any object,
  7 objects will be distributed between two persons
  no. of ways of distributing 7 objects between two persons= 7c1+7c2+7c3+7c4+7c4+7c5+7c6+7c7 = 126
  also two persons can be selected in 3c2 i.e 3 ways
  so total no. of ways of distributing objects when 1 person does not get any object= 3*126=378
  when two person does not get any object, all d 7 objects will be given to 1 person.. and this 0ne person can be selected from 3 persons in three ways..
  so total no. of required ways = 378+3= 381
• 9 years agoHelpfull: Yes(3) No(0)
• using formula n+r-1Cr-1
  7+3-1C3-1= 9C2
  ans. 36
• 9 years agoHelpfull: Yes(2) No(11)