In how many ways can 7 different objects be divided among 3 persons so that either one or two of them do not get any object?

• Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.
  
  Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.
  
  a) A gets 6. B gets 1. 7 ways.
  b) A gets 5. B gets 2. 21 ways.
  c) A gets 4. B gets 3. 35 ways.
  d) A gets 3. B gets 4. 35 ways.
  e) A gets 2. B gets 5. 21 ways.
  f) A gets 1. B gets 6. 7 ways.
  Total = 126 ways to divide 7 items between A & B.
  Total number of ways for case 2 = 126*3 = 378 (Either A, or B, or C don't get anything).
  
  Answer = Case 1 + Case 2 = 3 + 378 = 381
• 10 years agoHelpfull: Yes(120) No(11)
• 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+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(38) No(2)
• 3*(2^7-1)=381
• 10 years agoHelpfull: Yes(14) No(7)
• ans will be 84
  see how..
  at first two persons are getting something and third one not..and this can be done in 3 ways.. so.. 7C2 *3 =63 and now consider 2 of them are not having anything .so 7C1 *3(as this can also be done in 3 ways) so as a um 63 +21 =84.
  
• 10 years agoHelpfull: Yes(8) No(26)
• answer is 21 ways
  case 1:(7,0,0)=3!/2!=3 ways
  case 2:(1,6,0)=3!=6 ways
  (2,5,0)=6 ways
  (3,4,0)=6 ways
  so, total=3+6+6+6=21 ways
• 10 years agoHelpfull: Yes(5) No(21)
• @SATISH : your answer is right can u explain me how you got 7,21,35...etc
• 10 years agoHelpfull: Yes(5) No(1)
• @VARSHA
  7c6,7c5,7c4,7c3,7c2,7c1
• 10 years agoHelpfull: Yes(4) No(5)
• 7C3-7C2-7C1
  = 7
• 10 years agoHelpfull: Yes(3) No(15)
• only satish right
• 10 years agoHelpfull: Yes(2) No(2)
• shrinivas ji
  A gets 6 so 7C6 and B gets 1 so 7C1 then u will get 7C6+7C1=7 do it other like this also..
• 10 years agoHelpfull: Yes(2) No(10)
• hello can anyone explain me how the ways are calculated in case 2.pls explain its confusing ..thanks in advance..
• 9 years agoHelpfull: Yes(2) No(0)
• 7C1+7C2+7C3+7C4+7C5+7C6+7C7=127
  127*3=381 ways
• 8 years agoHelpfull: Yes(2) No(0)
• 7C6+7C5+7C4+7C3+7C2+7=126
  Now, there are 126 ways to divide 7 objects among 3 people. Hence, 126*3=378
• 9 years agoHelpfull: Yes(1) No(1)
• 8c2=8!/2!*6!
• 10 years agoHelpfull: Yes(0) No(3)
• 42
  7p2+7p1=42
• 10 years agoHelpfull: Yes(0) No(4)
• Answer is 216
  
• 10 years agoHelpfull: Yes(0) No(4)
• rajan ka shai h bhai...84
• 10 years agoHelpfull: Yes(0) No(6)
• 
  
  how this 7 ways comes i dont how can you explain steps?
  
  a) A gets 6. B gets 1. 7 ways.
  b) A gets 5. B gets 2. 21 ways.
  c) A gets 4. B gets 3. 35 ways.
  d) A gets 3. B gets 4. 35 ways.
  e) A gets 2. B gets 5. 21 ways.
  f) A gets 1. B gets 6. 7 ways.
  
• 10 years agoHelpfull: Yes(0) No(0)
• case1: 1 person do not get any object
  select 2 persons from 3 persons to give object=3c2=3
  The no of ways of giving 7 different objects to 2 persons=7c1+7c2+7c3+7c4+7c5+7c6+7c7=126
  so no of ways =126*3=378
  case2: 2 persons do not get anything
  select 1 person among 3 persons =3c1=3
  giving 7 different objects to 1 person=1 way
  no of ways=3*1=3
  
  Total no of ways to to divide 7 different objects among 3 persons in a given
  condition 378+3 =381
  
  Ans) 381
• 8 years agoHelpfull: Yes(0) No(0)
• Case1: - When one of them do not get any object. That means 2 people will get it.
  So No. ways to select 2 persons out of 3 is 3C2.
  Now No. ways by which 7 objects can be distributed among 2 persons= 27
  In this we have to eliminate the terms where either of them didn’t get any object. There only two times either of them didn’t get any object.
  So the required no. of ways= 3C2. (27-2)
  Case2: - When two of them do not get any object. That means only 1 will get all of it.
  So no. of ways to select 1 person= 2C1
  No. of ways to distribute 7 objects among 1 = 17
  So the required no. of ways = 2C1. 17
  Total no ways = 3C2. (27-2) + 2C1. 17 = 381
• 7 years agoHelpfull: Yes(0) No(0)
• 7c1+7c2+7c3+7c4+7c5+7c6+7c7=127
  127*3=381
• 6 years agoHelpfull: Yes(0) No(0)
• Love you too kishore
• 5 years agoHelpfull: Yes(0) No(0)
• Love you too kishore
• 5 years agoHelpfull: Yes(0) No(0)