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In how many ways can Nicole distribute 20 chocolates among B

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Intern
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In how many ways can Nicole distribute 20 chocolates among B [#permalink] New post 11 Dec 2013, 01:02
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

33% (02:20) correct 67% (00:49) wrong based on 51 sessions
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] New post 11 Dec 2013, 02:33
Expert's post
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] New post 11 Dec 2013, 02:38
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
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Re: In how many ways can Nicole distribute 20 chocolates among B [#permalink] New post 11 Dec 2013, 04:07
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] New post 02 May 2014, 01:20
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This post received
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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
Re: In how many ways can Nicole distribute 20 chocolates among B   [#permalink] 02 May 2014, 01:20
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