Latest TCS Aptitude Question SOLUTION: In how many ways can 7 distinct objects be divided among three people so that either one or two of them do not get any object?

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

Asked In TCS Diksha Kumari (8 years ago)

Solved Pooja Shaw Read Solution (7)

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Read Solution (7) :

Pooja Shaw  (8 years ago) Best Solution

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

Is this solution Helpfull? Yes (32) | No (9)  

neelesh kumar dwivedi  (8 years ago)

assume there are three persons A,B ,C
now consider following two cases
1.
A do not get anything
in this case 7 objects can be distributed between B and C as follows
B C
1 6 - total ways are 7!/1!*6!=7
2 5 -total ways are 7!/2!*5!=21
3 4 - total ways are 7!/3!*4!=35
4 3 - total ways are 7!/4!*3!=35
5 2 - total ways are 7!/5!*2!=21
6 1 - total ways are 7!/6!*1!=7
hence total ways of distributing objects between B and C = 126
similarly for (A c)and(AB) each =126
CASE2-
two persons do not get anything
in thi case there will be three waya these are
007 ,070 ,700
combining both the cases
total no of ways =126*3+3=381

Is this solution Helpfull? Yes (17) | No   

harshit singh  (8 years ago)

assuming person C is empty handed
1st object can be distributed to 2 person
similarly 2nd,3rd,4th,5th,6th,7th
no of ways =2*2*2*2*2*2*2
now assuming B &a as empty handed
total ways=3*2^7-3 =381
we subtracted 3 ,becoz there is conidtion when only 1 person get the object is repeated twice i.e 6 instead of 3

Is this solution Helpfull? Yes (3) | No (1)  

abha bharti  (8 years ago)

36 is the answer

Is this solution Helpfull? Yes (1) | No (6)  

Subhajit Mazumdar  (8 years ago)

7c2+7c1=28 is answr

Is this solution Helpfull? Yes (1) | No (3)  

mugdha bhatia  (8 years ago)

1st situation:
when 2 of them don't get any object i.e. all 7 are given to 1 of them . so there can be 1 out of 3 which gets all so , 3 ways.

2 situation :
when one of them doesn't get any of the objects i.e. 7 objects are divided between two of them . Since these 7 are distinct objects so choices are also made that which object is given to which guy of the two.

so,
7c1+7c2+7c3+7c4+7c5+7c6=126 ways.
Now this is the no. of ways in which objects are divided between 2 of them
Now we can also select these two of the 3
so we have 3 choices
so final ans is:
3*126+3=381.

Is this solution Helpfull? Yes (1) | No (1)  

Ritendra Pratap Singh  (4 years ago)

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

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