Latest TCS Aptitude Question SOLUTION: 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?

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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?

Asked In TCS Niveditha Ravichandran (9 years ago)

Solved satish Read Solution (23)

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Read Solution (23) :

satish  (9 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 (120) | No (11)  

Manpreet Kaur  (9 years ago)

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

Is this solution Helpfull? Yes (38) | No (2)  

shubham patidar  (9 years ago)

3*(2^7-1)=381

Is this solution Helpfull? Yes (14) | No (7)  

ranjan kumar  (9 years ago)

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.

Is this solution Helpfull? Yes (8) | No (26)  

amit agrawal  (9 years ago)

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

Is this solution Helpfull? Yes (5) | No (21)  

Varsha  (9 years ago)

@SATISH : your answer is right can u explain me how you got 7,21,35...etc

Is this solution Helpfull? Yes (5) | No (1)  

Niveditha Ravichandran  (9 years ago)

@VARSHA
7c6,7c5,7c4,7c3,7c2,7c1

Is this solution Helpfull? Yes (4) | No (5)  

Souradip Nath  (9 years ago)

7C3-7C2-7C1
= 7

Is this solution Helpfull? Yes (3) | No (15)  

abhisek banerjee  (9 years ago)

only satish right

Is this solution Helpfull? Yes (2) | No (2)  

priyanka jain  (9 years ago)

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..

Is this solution Helpfull? Yes (2) | No (10)  

pradeep kumar  (9 years ago)

hello can anyone explain me how the ways are calculated in case 2.pls explain its confusing ..thanks in advance..

Is this solution Helpfull? Yes (2) | No   

LAKKUMANAN K  (7 years ago)

7C1+7C2+7C3+7C4+7C5+7C6+7C7=127
127*3=381 ways

Is this solution Helpfull? Yes (2) | No   

Chirantan   (8 years ago)

7C6+7C5+7C4+7C3+7C2+7=126
Now, there are 126 ways to divide 7 objects among 3 people. Hence, 126*3=378

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

akshitha  (9 years ago)

8c2=8!/2!*6!

Is this solution Helpfull? Yes | No (3)  

Manas Patra  (9 years ago)

42
7p2+7p1=42

Is this solution Helpfull? Yes | No (4)  

Jayaseelan  (9 years ago)

Answer is 216

Is this solution Helpfull? Yes | No (4)  

dhruv  (9 years ago)

rajan ka shai h bhai...84

Is this solution Helpfull? Yes | No (6)  

srinivas  (9 years ago)

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.

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Idemakanti Madhuri  (7 years ago)

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

Is this solution Helpfull? Yes | No   

Nikhil  (6 years ago)

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

Is this solution Helpfull? Yes | No   

varsha vinayak bhawar  (5 years ago)

7c1+7c2+7c3+7c4+7c5+7c6+7c7=127
127*3=381

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  (4 years ago)

Love you too kishore

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  (4 years ago)

Love you too kishore

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