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# In how many ways can X distribute 20 chocolates among A,B,C

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Manager
Joined: 05 Jul 2009
Posts: 181

Kudos [?]: 53 [0], given: 5

Re: PS: permutation - combinations [#permalink]

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17 Sep 2009, 16:25
WOW!!! Great Idea and great thread!!! Thanks.

Kudos [?]: 53 [0], given: 5

Senior Manager
Joined: 27 May 2012
Posts: 427

Kudos [?]: 90 [0], given: 487

Re: In how many ways can X distribute 20 chocolates among A,B,C [#permalink]

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13 Aug 2013, 03:20
swath20 wrote:
In how many ways can X distribute 20 chocolates among A,B,C and D

(I) If each receives atleast one

(II) If X may chose to give no chocolates to whom he dislikes on that particular day.

Seems as though the answer is D to this one though both the options contradict each other

(I) If each receives atleast one:

Number of ways to distribute n things among r people so that each receive at least one
$$\hs{10mm} C^{n-1}_{r-1}\hs{10mm} = C^{19}_{3}$$

(II) If X may chose to give no chocolates to whom he dislikes on that particular day.
Number of ways to distribute n things among r people so that each receive 0 to n things

$$C^{n+r-1}_{r-1}\hs{10mm} = C^{23}_{3}$$

Please do correct if I am making a mistake somewhere.
Thanks
_________________

- Stne

Kudos [?]: 90 [0], given: 487

Re: In how many ways can X distribute 20 chocolates among A,B,C   [#permalink] 13 Aug 2013, 03:20

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