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The subsets of the set {s, t, u} consisting of the three [#permalink]

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27 Nov 2012, 00:54

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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, 02:43, edited 1 time in total.

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).

Re: The subsets of the set {s, t, u} consisting of the three [#permalink]

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29 Nov 2012, 01:52

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).

Answer: E.

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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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).

Answer: E.

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]

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29 Nov 2012, 05:58

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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If you found my post useful and/or interesting - you are welcome to give kudos!

Thanks Bunuel, i got it, but do you think the way of thinking was correct?

Yes, your approach is 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.

Re: The subsets of the set {s, t, u} consisting of the three [#permalink]

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12 May 2014, 14:22

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?

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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