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In how many ways can Nicole distribute 20 chocolates among B

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

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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

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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
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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, 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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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 02 May 2014, 02:20
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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 01 Aug 2016, 02:06
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Re: In how many ways can Nicole distribute 20 chocolates among B [#permalink]

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New post 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).

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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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