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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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Question Stats:

74% (01:13) correct 26% (01:22) wrong based on 46 sessions

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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. \(64\)

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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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Collection of Questions:
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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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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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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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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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New post 18 Sep 2017, 21:26
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Re: M28-29 [#permalink]

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New post 02 Jun 2018, 20:11
Hi Bunuel,

I was trying to solve this question by the slot method but I am not getting it right.

Since there are are 3 spaces that need to be filled, we have three slots. The first slot could have either of the 7 letters or a blank, second slot could have either of the 6 letters or a blank and so on... And since we have 3 slots, divide that by 3!.

(8*7*6)/3! = 56

The empty set should be accounted for within this as well. So, according to me, this should have been the end of it but that's wrong of course. Can you please tell me what I am missing?

Thanks in advance.
Re: M28-29   [#permalink] 02 Jun 2018, 20:11
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