Cool Combinatorics!!

Probability Level 3

Find the number of ways in which 4 4 identical balls can be distributed among 6 6 identical boxes,if not more than 1 1 ball goes into each box.


The answer is 1.

Anik Mandal by Anik Mandal , 21, India

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3 solutions

Jaikirat Sandhu
Jan 27, 2015

All the balls are same as well as all boxes are same too. :P

2 Helpful 0 Interesting 0 Brilliant 0 Confused

i dnt get it.. can u explain again

Nithin Nithu - 6 years, 2 months ago
Rama Devi
Jun 4, 2015

Both the balls and boxes are similar.Therefore the number of ways is 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Wrong. Balls and boxes are not the same thing.

Anik Mandal
Jan 24, 2015

No.of identical balls= 4 4 No.of identical boxes= 6 6

Now,distributing 4 4 identical balls among 6 6 identical boxes when not more than one ball goes into a box,implies to select 4 4 boxes from among 6 6 boxes,which can be done in ( 6 4 ) = 15 \binom{6}{4}=15

Hence the answer..

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Your approach seems to suggest that the boxes are distinct? Otherwise, the only way is to have 4 boxes of 1 ball each.

Calvin Lin Staff - 6 years, 4 months ago

then why is the correct answer 1?

Terrell Bombb - 4 years, 10 months ago

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