7 different objects divided among 3 persons .in how many ways this can be done if atleast one of them gets exactly one object?

• This is a case of atleast.
  So formula used is n-1 C r-1
  so 6 c 2 =15 ans
• 10 years agoHelpfull: Yes(27) No(26)
• Guys this is the exact same ques in Arun Sharma LOD 3 of P&C Q No 25. For those who do not have it here is the answer
  If only one gets 1 object
  The remaining can be distributed as (6,0),(4,2),(3,3).
  (7C1 * 6C6 *3! )+(7C1 * 6C4 * 3!)+(7C1 * 6C3 * 3!/2! )=42+630+420=1092 ways
  
  If 2 people gets one object each
  7C1*6C1*5C3*3!/2!=126
  
  So total ways =1092+126=1218
  
  PS- For those who think n-1Cr-1 is d ans rem its only applicable with non identical objects not with identical ones
• 10 years agoHelpfull: Yes(26) No(1)
• n=7-3=4,r=3,n+r-1Cr-1=(4+3-1)C(3-1)=15
• 10 years agoHelpfull: Yes(12) No(16)
• the actual formula for this kind of questions are: objects-1 C persons-1 will give you the solution
• 10 years agoHelpfull: Yes(3) No(4)
• _ _ _ these are 3 persons
  1 _ _ (1 denotes 1st person getting exactly 1 object)
  _ 1 _
  _ _ 3 so 3 ways (3)
  taking 1 _ _ and then multiplying by 3
  1 _ _
  _ _ can have values (where value no. denotes no. of objects)
  1,5 --> 6 (6 ways(type of objects) to distribute object to 2nd person)
  2,4 --> 15
  3,3 --> 20
  4,2 --> 15
  5,1 --> 6
  as all objects are distinct..
  total is 6+15+20+15+6=(62)
  1 in (1 _ _) can have 7 type of objects..
  no. of ways = 62*7
  as there are 3 cases {1 _ _, _ 1 _, _ _ 1}
  62*7*3=1302 answer..
• 10 years agoHelpfull: Yes(2) No(8)
• ans=15
  simply use the formula n-1 C r-1
  6c2=15
• 10 years agoHelpfull: Yes(2) No(5)
• (3^7-1), is the answer....
• 10 years agoHelpfull: Yes(1) No(10)
• 7 objects for 3 prsons , thrfor the no. of ways= 3^7-1= ans
• 10 years agoHelpfull: Yes(1) No(7)
• one is fixed ...so there are 6 objects to be distributed among 2 people ...so first got 6 ways and the next got 5 ways .....ie 6p2 or 6*5
• 10 years agoHelpfull: Yes(1) No(6)
• _ _ _ these are 3 persons
  1 _ _ (1 denotes 1st person getting exactly 1 object)
  _ 1 _
  _ _ 1 so 3 ways (3)
  taking 1 _ _ and then multiplying by 3
  in 1 _ _
  _ _ can have values (where value no. denotes no. of objects)
  1,5 --> 6 (6 ways(type of objects) to distribute object to 2nd person)
  2,4 --> 15
  3,3 --> 20
  4,2 --> 15
  5,1 --> 6
  as all objects are distinct..
  total is 6+15+20+15+6=(62)
  1 in (1 _ _) can have 7 type of objects..
  no. of ways = 62*7
  as there are 3 cases {1 _ _, _ 1 _, _ _ 1}
  62*7*3=1302 answer..
• 10 years agoHelpfull: Yes(1) No(9)
• 1 _ _ : 7*2^6=7*64=448
  - 1 _ : 7*2^6=7*64=448
  _ _ 1 : 7*2^6=7*64=448
  ans= 448*3= 1344
• 10 years agoHelpfull: Yes(1) No(5)
• ans 3^7-3
  total ways=3^7
  3=ways of giving a object from any one of them and other 2 empty
  
• 10 years agoHelpfull: Yes(0) No(5)
• yes amar singh u r correct..i didn't consider that a person can have 0 no. of objects also..answer from my point of view is 1344 :)
  instead of only taking cases 1,5,,2,4,,3,3,,.. we sholud also take 1,0,6,, 1,6,0,, 0,1,6,, 6,1,0,, 0,6,1,, 6,0,1 total is 6
  multipying by 7 as no. of distinct objects are 7..i.e. 42
  1302+42=1344
• 10 years agoHelpfull: Yes(0) No(2)
• Sry I meant for those who think n-1Cr-1 is d ans rem its only applicable with identical objects not with identical ones and here is non identical i.e unique
• 10 years agoHelpfull: Yes(0) No(0)
• Let up denote the persons as
  A,B,C
  now when A gets 1 the remaining 6 objects can be divided in 6P2 ways
  continuing in this way you will get two more cases in which B gets 1 and another in which C gets one
  therefore total no. Of ways =6P2+6P2+6P2
  =3*6P2
  =3*30=90 ways
• 9 years agoHelpfull: Yes(0) No(0)
• a'+1+b'+1+c'+1=7
  a'+b'+c'=4
  therefore 4 times 1 and 2 partitions of divisions
  1111pp
  6c2=15 ans
• 8 years agoHelpfull: Yes(0) No(0)