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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: 23

Kudos [?]: 5 [1], given: 27

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

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11 Dec 2013, 02:02
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Question Stats:

40% (00:50) correct 60% (01:08) wrong based on 149 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
[Reveal] Spoiler: OA

Kudos [?]: 5 [1], given: 27

Math Expert
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129406 [0], given: 12201

Re: In how many ways can Nicole distribute 20 chocolates among B [#permalink]

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11 Dec 2013, 03:33
Expert's post
1
This post was
BOOKMARKED
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 $$n-1C_{r-1}$$.

Thus the answer is 19C3.

Answer: B.

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

Kudos [?]: 129406 [0], given: 12201

Math Expert
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129406 [0], given: 12201

Re: In how many ways can Nicole distribute 20 chocolates among B [#permalink]

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11 Dec 2013, 03:38
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 $$n-1C_{r-1}$$.

Thus the answer is 19C3.

Answer: B.

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

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Hope this helps.
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Kudos [?]: 129406 [0], given: 12201

Intern
Joined: 19 Mar 2013
Posts: 23

Kudos [?]: 5 [0], given: 27

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!

Kudos [?]: 5 [0], given: 27

Manager
Joined: 28 Jul 2013
Posts: 85

Kudos [?]: 42 [1], given: 37

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
This post received
KUDOS
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

Kudos [?]: 42 [1], given: 37

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16543

Kudos [?]: 274 [0], given: 0

Re: In how many ways can Nicole distribute 20 chocolates among B [#permalink]

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01 Aug 2016, 02:06
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]

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10 Sep 2017, 14:37
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: In how many ways can Nicole distribute 20 chocolates among B   [#permalink] 10 Sep 2017, 14:37
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# In how many ways can Nicole distribute 20 chocolates among B

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