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18 Nov 2006 03:14:59 IST

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Contest [swordfish #3]: Find ways to distribute identical balls in identical boxes

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Find the no. of ways of distributing 30 identical balls in the three identical boxes, such that no box remains empty.

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punit grewal

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26 Nov 2007 12:55:55 IST

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Solve this

raja mukh

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26 Nov 2007 15:27:07 IST

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As all the balls are identical and each box must have a ball (i.e. none is empty), the problem boils down to C(29,2)= 406

mirza baig

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26 Nov 2007 17:37:34 IST

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Q:find the number of ways to distribute 30 identical balls in to 3 boxes.that no box is remain empty.

ANS:30 objects can be put in 3 boxes in 3 ways .and each box remain is empty is in

3 -3 ways

ABHILASH CHENREDDY

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26 Nov 2007 19:53:13 IST

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this can be done by using combinations.

the balls can be arranged in 30_c3ways and as all balls and boxes are identical there will be no repetetions . so answer is 30c3

-abhilash

nishant singh

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26 Nov 2007 22:03:49 IST

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well let's 30 balls in a row ,
29 places between 30 balls

let's take 2 sticks to be kept in these 29 places, by keeping 2 sticks we divide balls in 3 parts , and we can keep each part in individual boxes

so problem is basically no. of ways of keeping 2 identical sticks in 29 places

the answer is 29C2 = 29*28/2 = 406 ways,

ABHILASH CHENREDDY

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28 Nov 2007 19:56:58 IST

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the answer is 30_c3

because all are identical

kishor kumar ummidi

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29 Nov 2007 14:38:43 IST

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the answer is 29C2 = 406

KUSHAL AGARWAL

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18 Jan 2008 16:47:47 IST

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29C2

Priyesh

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18 Jan 2008 17:40:44 IST

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according to me

all the above are wrong except chandrashekhar sir & aspiredtolive.

the answer is 75

refer to page 4 (soln. by aspiredtolive)

bhargav kumar reddy

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30 Jan 2008 21:14:29 IST

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first place 3 things in 3 places in one way .
then remaining 27 can be distributed in

3²⁷- 3c1 2²⁷ + 3c2 ways

RAHUL GAADHE

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9 Feb 2008 19:55:19 IST

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IMAGINE 30 DOTS &WE HAVE TO PUT 2BARS IN BETWEEN THEM

SO TOTAL NO OF WAYS 29C2(NO OF BALLS IN EACH BOX>0

Ranjeet Panda

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9 Feb 2008 20:05:02 IST

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ya porshe is correct
nice approach

Bhaskar Tetarbe

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9 Feb 2008 20:13:26 IST

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Let us first fill all the 3 boxes with 3 identical balls which can be filled in 1 way.
Now if all the balls are necessary to be distributed then,
there is all in all ²⁷C₃ ways to distribute all the identical balls.

nitigya

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9 Feb 2008 20:14:35 IST

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we hv 30 identical balls and hv 3 identical markers(or boxes) as boXes should hv at least 1 ball ,the effective space for markers to be placed are 29

hence ²⁹C₃

Celestine Preetham

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30 Apr 2008 20:43:25 IST

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IS THE ANS 3^29 /2 - 1

Ankit Mahato

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31 May 2008 07:48:36 IST

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arrange in a row 30 balls and calculate the no. of ways to put 2 partions in 29 places in between

Ans : ²⁹C₂

abhishek raj

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31 May 2008 08:56:01 IST

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place one ball each in each of the boxes nd then distribute the other 27 randomly....the number of ways of doing this is 29C2 ways......but the boxes are identical so the final answer will become.......29C2/3

SUNDEEP ALLAMRAJU

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31 May 2008 09:46:16 IST

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First supply each box with one ball.The remaining 27 balls can be distributed by taking them along with 2 other identical things and arranging in a row in 29!/27!2!=29c₂ ways.Since the boxes are identical,The same partitions are considered as one.So,the no. of ways are 29c₂/3

ravi teja

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31 May 2008 13:59:22 IST

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I think it is 30C3 and it will be uniform distribution and maximum no.of distribution.
plzzz..........corrct me if i m wrong........

ravi teja

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31 May 2008 14:00:55 IST

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if we take equal distribution den d no.of arrangements will be 10x10x10=1000 ways

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