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The subsets of the set {s, t, u} consisting of the three

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The subsets of the set {s, t, u} consisting of the three [#permalink]  26 Nov 2012, 23:54
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The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Last edited by Bunuel on 27 Nov 2012, 01:43, edited 1 time in total.
Renamed the topic and edited the tags.
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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  27 Nov 2012, 02:02
Expert's post
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  29 Nov 2012, 00:52
Bunuel wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?
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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  29 Nov 2012, 01:59
Expert's post
ziko wrote:
Bunuel wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?

You are forgetting an empty set, which is also a subset of {s, u, w, x} and do not contain t.
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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  29 Nov 2012, 04:58
I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?[/quote]

You are forgetting an empty set, which is also a subset of {s, u, w, x} and do not contain t.[/quote]

Thanks Bunuel, i got it, but do you think the way of thinking was correct?
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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  29 Nov 2012, 07:27
Expert's post
ziko wrote:
Thanks Bunuel, i got it, but do you think the way of thinking was correct?

# of subsets with 4 elements is 1: $$C^4_4=1$$;
# of subsets with 3 elements is 4: $$C^3_4=4$$;
# of subsets with 2 elements is 6: $$C^2_4=6$$;
# of subsets with 1 elements is 4: $$C^1_4=4$$;
plus 1 empty set.

1+4+6+4+1=16.
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Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  12 May 2014, 13:22
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

I thought that the formula for number of subsets for n elements was 2^n -1

Can anybody explain why this formula does not apply in this case?

Thanks!
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 29791
Followers: 4899

Kudos [?]: 53544 [0], given: 8165

Re: The subsets of the set {s, t, u} consisting of the three [#permalink]  13 May 2014, 00:03
Expert's post
jlgdr wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

I thought that the formula for number of subsets for n elements was 2^n -1

Can anybody explain why this formula does not apply in this case?

Thanks!
Cheers
J

The number of subsets of a set with n elements is 2^n, including an empty set.
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Re: The subsets of the set {s, t, u} consisting of the three   [#permalink] 13 May 2014, 00:03
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