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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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rosey

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20 Nov 2006 16:47:52 IST

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i think,
when balls as well as boxes are identical,the number of combinations and arrangements will be 1 each in 12 cases.
therefore, the required number of ways
=1x1x12=12 ways

rosey

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20 Nov 2006 16:53:23 IST

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12 cases means, the balls can be distributed in ,1,1 29 ; 1 2 28; ,,,,,,,,,,,,,,,,,,,and soon

Manasi

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2 Dec 2006 12:34:19 IST

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for each box minimum no of balls that shud b kept is 1 n maximum is27... so applying the thrfore total no of ways= coeffecient of t³⁰ in expansion of ( t¹+ t²+....... +t²⁷) ³

this will give the answer....

2569497

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3 Dec 2006 19:23:19 IST

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give the 29 balls 29 peoples and last ball give to the last man with the box

2569497

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3 Dec 2006 19:27:10 IST

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give 27 balls to 27 peoples and the last 3 balls give the other peoples with the boxes.

nikunj_94

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5 Dec 2006 02:15:31 IST

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WE HAVE 30 BALLS AND WE HAVE TO DIVIDE THEM INTO THREE GROUPS.
THIS CAN BE DONE BY PLACING TWO MARKERS BETWEEN THEM.
. . . . .
No. of spaces = 29
Ways of placing two markers= ²⁹C₂^{BUT SINCE THE BOXES ARE IDENTICAL SO TOTAL NO. OF CASES WII BE ONE-THIRD
=} (²⁹C₂ )/3

bhuvnesh2007

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6 Dec 2006 19:31:58 IST

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15,10,5

gorakavipraveen

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6 Dec 2006 19:52:04 IST

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first off all supplying 3 balls to 3 boxes. Remaining are 27balls. Consider a box. It can collect 1,2,3,4,........27 balls with it. Hence 27 casses possible with a box. NO MATTER WHAT THE BOX IT IS since all boxes are identical. So the answere must be 27.

Mohitshah

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6 Dec 2006 23:29:32 IST

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the ans shud be

30! / (27! * 3!)

Uday Prakash

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7 Dec 2006 22:11:32 IST

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³⁰_{^C3 IT'S EASY}

anusha_drg2002

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9 Dec 2006 20:30:16 IST

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29x28/30x29=28/30=14/15

prashanth

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10 Dec 2006 18:21:29 IST

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to solve this sum we can use combinations

the answer would be 30C3 i.e, 4060 different ways

vibhu2006

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14 Dec 2006 09:47:48 IST

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10 each

richeek

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14 Dec 2006 12:16:08 IST

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the no of soln is is any one get any no of balls
30+3-1
C
3-1
=32
C
2
=32.31/2=16.31=496
furthur cases when some donot get balls are present
3c2+3c2+3c3=7
therefore answer is 496-7=489

anshulnigam

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14 Dec 2006 13:49:31 IST

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the answer is 30c3 ie 4060

someshyechury

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14 Dec 2006 13:51:44 IST

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28*3=84 ways
ans..84 ways

raghvendrakannao

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15 Dec 2006 13:21:40 IST

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The answer is ³⁰c₃-²⁹c₂-²⁸c₁ which is equel to 56,406

raghvendrakannao

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15 Dec 2006 13:28:16 IST

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The answer is ³⁰c₃-²⁹c₂-²⁸c₁which is equal to 3626

richeek

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15 Dec 2006 15:15:31 IST

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the no of soln is is any one get any no of balls
30+3-1
C
3-1
=32
C
2
=32.31/2=16.31=496
furthur cases when some donot get balls are present
3c2+3c2+3c3=7
therefore answer is 496-7=489

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