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M28-29

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M28-29 [#permalink]

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New post 16 Sep 2014, 01:29
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Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. \(29\)
B. \(56\)
C. \(57\)
D. \(63\)
E. \(64\)
[Reveal] Spoiler: OA

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Re M28-29 [#permalink]

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New post 16 Sep 2014, 01:29
Official Solution:

Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. \(29\)
B. \(56\)
C. \(57\)
D. \(63\)
E. \(64\)


1 empty set;

\(C^1_7=7\) sets with one element;

\(C^2_7=21\) sets with two elements;

\(C^3_7=35\) sets with three element.

Total 1+7+21+35=64 sets.


Answer: E
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Resources:
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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?
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Re: M28-29 [#permalink]

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New post 12 Mar 2016, 14:32
Why doesn't for example AB and BA count as a different subset?? No where in the problem says that order doesn't matter.

Someone please help enlighten me - thank you!
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Re: M28-29 [#permalink]

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New post 13 Mar 2016, 08:26
happyface101 wrote:
Why doesn't for example AB and BA count as a different subset?? No where in the problem says that order doesn't matter.

Someone please help enlighten me - thank you!


A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
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Re: M28-29 [#permalink]

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New post 03 Apr 2017, 03:24
We dont we count the empty set too? So 65?

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New post 03 Apr 2017, 03:28

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Re: M28-29 [#permalink]

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New post 18 Sep 2017, 18:40
Bunuel, I actually do not understand what "an empty set" means. Could you please explain?

Thanks.
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Re: M28-29 [#permalink]

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New post 18 Sep 2017, 21:26

Kudos [?]: 128443 [0], given: 12173

Re: M28-29   [#permalink] 18 Sep 2017, 21:26
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