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In how many ways can Nicole distribute 20 chocolates among B

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

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New post 11 Dec 2013, 02:02
1
6
00:00
A
B
C
D
E

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

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New post 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 \(n-1C_{r-1}\).

Thus the answer is 19C3.

Answer: B.

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


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

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

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New post 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 \(n-1C_{r-1}\).

Thus the answer is 19C3.

Answer: B.

P.S. Does not seem that this question is from reliable GMAT source...
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Re: In how many ways can Nicole distribute 20 chocolates among B  [#permalink]

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

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New post 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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