Latest TCS Aptitude Question SOLUTION: In how many 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 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 HARSHIT SHUKLA (9 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

garima chhabra  (9 years ago)

if one person is given no object then the number of ways of distributing objects among rest of the two would be:
2*(7C1 + 7C2 + 7C3)
which is 378
and the number of ways only one person gets all object is 3
so total ways are 378+3=381

Is this solution Helpfull? Yes (14) | No (3)  

Mahesh  (9 years ago)

3c1*((2^7)-2)=378

Is this solution Helpfull? Yes (2) | No (1)  

Antara Daftary  (9 years ago)

Whn two do not get nythn::
A B C
7 :1 way
7 :1 way
7 :1 way
total 3 ways
when 1 do not get nythn::
6 1 :1 way
1 6 :"
6 1 :"
1 6 :"
6 1 :"
1 6 :"
so total for 6&1=6 ways
similarly for 5&2=6 ways
similarly for 4&3=6 ways
so total=3+6+6+6=21 ways

Is this solution Helpfull? Yes (1) | No   

Deep Chandra  (9 years ago)

381 is correct answer

Is this solution Helpfull? Yes (1) | No   

shambhu  (8 years ago)

if one person gets no object then remaining two will get objects in following ways :
3C2*(2^7-2)
if two persons gets no object then remaining one persons gets all objects in ways:
3C1*1
So, total no of ways = 3C2*(2^7-2) + 3C1*1 = 381

Is this solution Helpfull? Yes (1) | No   

vivek kumar  (9 years ago)

num of ways so that one person get nothing= 3c1*((2^7)-2))=368
num of ways so that 2 person get nothing= 3c2*1=3
so total num of ways=368+3=371

Is this solution Helpfull? Yes | No (2)  

sushma  (9 years ago)

x1+x2...+x7=3
so for (n+r-1)c(r-1)=3+7-1c6=9c6=168

Is this solution Helpfull? Yes | No (1)  

Tanmoy Sen  (9 years ago)

ans
n+r-1Cr-1 (n=7 , r = 3) = 36 ?

Is this solution Helpfull? Yes | No (2)  

SK IMRAN   (9 years ago)

can any one tell me why following process is not right??? i am not able to understand....

(6c1*5c1*4c1*3c1)(14c1)/18c5=10/17

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Nikhil   (8 years ago)

Case 1: when one of them do not get any object, then the objects will be divided among 2 persons.

No. of ways to select 2 persons = 3C2

No. of ways to divide 7 objects among 2 persons = 27

So required no. of ways= 3C2(27 - 2) = 378 [when none of them get any object]
Case 2: when objects are given to only one person.

Required. no. of ways= 3C1 = 3.

So, total no. of ways = 378+3 = 381

Hence 381is the correct answer.

Is this solution Helpfull? Yes | No   

Nikhil   (8 years ago)

Case 1: when one of them do not get any object, then the objects will be divided among 2 persons.

No. of ways to select 2 persons = 3C2

No. of ways to divide 7 objects among 2 persons = 2^7

So required no. of ways= 3C2(2^7 - 2) = 378 [when none of them get any object]
Case 2: when objects are given to only one person.

Required. no. of ways= 3C1 = 3.

So, total no. of ways = 378+3 = 381

Hence 381is the correct answer.

Is this solution Helpfull? Yes | No   

Nikhil   (8 years ago)

. Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.

Division of m+n+p objects into three groups is given by (m+n+p)!m!×n!×p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!×3!×3!×12! + (7)!1!×2!×4! + (7)!1!×1!×5!×12! = 70 + 105 + 21 = 196

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