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# There are twenty-five identical marbles to be divided among four broth

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Manager
Joined: 25 Jan 2010
Posts: 103
Location: Calicut, India
There are twenty-five identical marbles to be divided among four broth  [#permalink]

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01 Sep 2010, 16:15
2
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:46) correct 33% (03:52) wrong based on 27 sessions

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There are twenty-five identical marbles to be divided among four brothers such that each one of them gets no less than three marbles. In how many ways can the marbles be divided among four brothers?

A) 286
B) 364
C) 455
D) 560
E) 650

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Re: There are twenty-five identical marbles to be divided among four broth  [#permalink]

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01 Sep 2010, 19:52
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cleetus wrote:
There are twenty-five identical marbles to be divided among four brothers such that each one of them gets no less than three marbles. In how many ways can the marbles be divided among four brothers?
A)286
B)364
C)455
D)560
E)650

Given each person should get atleast 3 marbles, hence distribute the three marbles (out of 25) to the 4 brothers. 12 marbles are distributed to 4 brothers.

Remaining marbles - 13. No of ways to distribute 13 marbles to 4 brothers such that each may get 0, 1, 2.... is $$16C3$$.

$$16C3$$ -- $$560$$.

[No of ways to distribute n identical items among r persons in which each person can get 0,1 or more items is
$$(n+r-1)C(r-1)$$]

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Re: There are twenty-five identical marbles to be divided among four broth  [#permalink]

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30 Jul 2017, 10:21
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Re: There are twenty-five identical marbles to be divided among four broth   [#permalink] 30 Jul 2017, 10:21
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