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

• Placement Papers
• /
• TCS
• /
• Numerical Ability
• /
• Permutation and Combination

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40025713) TCS Numerical Ability question Keep an EYE

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

Asked In TCS asxa asxaxax (10 years ago)

Unsolved Read Solution (16)

Is this Puzzle helpful?   (11)   (0) Submit Your Solution Permutation and Combination

Read Solution (16) :

Arpit Tantia  (10 years ago)

This is a case of atleast.
So formula used is n-1 C r-1
so 6 c 2 =15 ans

Is this solution Helpfull? Yes (27) | No (26)  

Vibhu Gaur  (10 years ago)

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

Is this solution Helpfull? Yes (26) | No (1)  

dinesh  (10 years ago)

n=7-3=4,r=3,n+r-1Cr-1=(4+3-1)C(3-1)=15

Is this solution Helpfull? Yes (12) | No (16)  

harsha vardhan veeturi  (10 years ago)

the actual formula for this kind of questions are: objects-1 C persons-1 will give you the solution

Is this solution Helpfull? Yes (3) | No (4)  

Palash Bansal  (10 years ago)

_ _ _ 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..

Is this solution Helpfull? Yes (2) | No (8)  

pulkit bansal  (10 years ago)

ans=15
simply use the formula n-1 C r-1
6c2=15

Is this solution Helpfull? Yes (2) | No (5)  

Vinil Gohil  (10 years ago)

(3^7-1), is the answer....

Is this solution Helpfull? Yes (1) | No (10)  

VIKASH KUMAR SHARMA  (10 years ago)

7 objects for 3 prsons , thrfor the no. of ways= 3^7-1= ans

Is this solution Helpfull? Yes (1) | No (7)  

R Srihari  (10 years ago)

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

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

Palash Bansal  (10 years ago)

_ _ _ 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..

Is this solution Helpfull? Yes (1) | No (9)  

Amar Singh  (10 years ago)

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

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

sandeep  (10 years ago)

ans 3^7-3
total ways=3^7
3=ways of giving a object from any one of them and other 2 empty

Is this solution Helpfull? Yes | No (5)  

Palash Bansal  (10 years ago)

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

Is this solution Helpfull? Yes | No (2)  

Vibhu Gaur  (10 years ago)

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

Is this solution Helpfull? Yes | No   

aninda  (9 years ago)

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

Is this solution Helpfull? Yes | No   

Kunal Vikram  (8 years ago)

a'+1+b'+1+c'+1=7
a'+b'+c'=4
therefore 4 times 1 and 2 partitions of divisions
1111pp
6c2=15 ans

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.