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M28-29

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Bunuel
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M28-29 [#permalink] New post   16 Sep 2014, 01:29
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Question Stats:

72% (01:32) correct 28% (01:53) wrong based on 148 sessions
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Set S contains 7 different letters. How many subsets of S, including the empty set, contain at most 3 letters?

A. \(29\)
B. \(56\)
C. \(57\)
D. \(63\)
E. \(64\)
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E
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Re: M28-29 [#permalink] New post   13 Mar 2016, 08:26
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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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Re M28-29 [#permalink] New post   16 Sep 2014, 01:29
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Official Solution:

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

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


Subsets of S, with at most 3 letters, will be:

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 elements.

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


Answer: E
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Re: M28-29 [#permalink] 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] New post   15 Oct 2023, 13:25
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M28-29 [#permalink]
15 Oct 2023, 13:25
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