Latest CAT Aptitude Question SOLUTION: In how many ways 4 distinct balls can be distributed in 3 identical boxes ?

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(#M40036973) CAT Numerical Ability question Probability Keep an EYE

In how many ways 4 distinct balls can be distributed in 3 identical boxes ?

Asked In CAT Saraswathy (10 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Dr.Dipin Singh  (10 years ago)

I think 14 ways are possible.

as all 3 boxes are identical, only pattern of distribution will change.

Distribution can be :
004.... one way only
013 ..... 4 ways of choosing single ball in a box
022..... 3 ways of choosing 2 pairs from 4 balls.
112 ....... 6 ways of choosing one pair from 4 balls

total 14 ways

Is this solution Helpfull? Yes (8) | No   

Sakthi Viswanathan  (10 years ago)

4C1+4C2+4C3=4+6+4=14.

Is this solution Helpfull? Yes (4) | No   

Nishant  (10 years ago)

4 ways
as all 3 boxes are identical, only pattern of distribution will change.

Distribution can be :
004
013
022
112

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

Karan  (10 years ago)

I think Dipin is right.
as all 3 boxes are identical, only pattern of distribution will change.

Distribution can be :
004.... one way only. As boxes are identical, it does not matter which box gets 4 balls.
013 ..... 4 ways of choosing single ball in a box.. As boxes are identical, it does not matter which box gets 3 balls. But which ball is left alone, that matters. so 4 combinations are possible.

022..... 3 ways of choosing 2 pairs from 4 balls....When 2 pairs are to be made from 4 balls,only 3 ways are possible. AB+CD, AC+BD, AD+BC; next combinations like BC+AD will be same as AD+BC listed earlier.
112 ....... 6 ways of choosing one pair from 4 balls; AB, AC, AD,BC,BD,CD

total 14 ways

Is this solution Helpfull? Yes (2) | No   

amrendra pratap singh  (10 years ago)

plz someone explain it properly

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

Mukesh Nayal  (10 years ago)

3^4 ways using n^r concept

Is this solution Helpfull? Yes | No (6)  

Ann Theressa  (10 years ago)

6 ways
(if you cannot leave a box empty)

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