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# In how many ways can Nicole distribute 20 chocolates among B

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Intern
Joined: 19 Mar 2013
Posts: 20
In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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11 Dec 2013, 02:02
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:07) correct 53% (01:24) wrong based on 143 sessions

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In how many ways can Nicole distribute 20 chocolates among Ben, Kate, Mark and Tom so that each receives at least one?

A. 20C4
B. 19C3
C. 21C4
D. 21C3
E. None of the answers is correct
Math Expert
Joined: 02 Sep 2009
Posts: 59589
Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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11 Dec 2013, 03:33
calmkeeper wrote:
In how many ways can Nicole distribute 20 chocolates among Ben, Kate, Mark and Tom so that each receives at least one?

A. 20C4
B. 19C3
C. 21C4
D. 21C3
E. None of the answers is correct

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is $$n-1C_{r-1}$$.

P.S. Does not seem that this question is from reliable GMAT source...
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Math Expert
Joined: 02 Sep 2009
Posts: 59589
Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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11 Dec 2013, 03:38
1
1
Bunuel wrote:
calmkeeper wrote:
In how many ways can Nicole distribute 20 chocolates among Ben, Kate, Mark and Tom so that each receives at least one?

A. 20C4
B. 19C3
C. 21C4
D. 21C3
E. None of the answers is correct

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is $$n-1C_{r-1}$$.

P.S. Does not seem that this question is from reliable GMAT source...

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Intern
Joined: 19 Mar 2013
Posts: 20
Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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11 Dec 2013, 05:07
The source is "Ultimate guide to GMAT math" by Jay Stewart

I got the same answer in the book, what interests me is the logic behind this formula. thx!
Manager
Joined: 28 Jul 2013
Posts: 62
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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02 May 2014, 02:20
1
B K M T
let us assume that B gets only 1 piece

hence 19 are left and from 19 three are to be chosen

Hence 1x19C3
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Joined: 09 Sep 2013
Posts: 13724
Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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03 Jun 2019, 06:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In how many ways can Nicole distribute 20 chocolates among B   [#permalink] 03 Jun 2019, 06:43
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