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How many two-element subsets of {1, 2, 3, 4} are there that do not con

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srijatverma
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How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   01 Nov 2016, 02:55
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How many two-element subsets of {1, 2, 3, 4} are there that do not contain the pair of elements 2 and 4?

(A) One
(B) Two
(C) Four
(D) Five
(E) Six
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D
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Bunuel
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   01 Nov 2016, 04:04
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srijatverma wrote:
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

(a) One
(b) Two
(c) Four
(d) Five
(e) Six


{1,2}, {1,3}, {1,4}, {2,3}, {3,4}.

Or: \(C^2_4-1=5\).

Answer: D.
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   15 Sep 2017, 02:46
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vs224 wrote:
Why we should not delete 2, one for (4,2) also

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A set, by definition, is a collection of elements without any order. While, a sequence, by definition, is an ordered list of terms.

4C2 = 6 is the number of different two-element subsets from {1, 2, 3, 4} without the order:


{1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}. Only 1 one subset, namely {2,4}, should be subtracted.
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   14 Sep 2017, 23:07
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Could you please explain why do you deduct one?
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   14 Sep 2017, 23:23
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e100 wrote:
Bunuel,
Could you please explain why do you deduct one?


4C2 is the number of ALL two-element subsets. We subtract one subset {2, 4} to get the desired number.
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   15 Sep 2017, 02:38
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Why we should not delete 2, one for (4,2) also

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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   15 Sep 2017, 12:00
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srijatverma wrote:
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

(a) One
(b) Two
(c) Four
(d) Five
(e) Six

You can list the subsets in about 30 seconds.

{1,2,3,4}

Two-element subsets that do not contain the pair of elements 2 and 4

Element 1 paired with each possibility
Element 2 paired with each possibility
Element 3 - same

{1,2}
{1,3}
{1,4}
{2,3}
{3,4}

There are 5 subsets that satisfy the conditions of the prompt.

Answer D
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   21 Sep 2017, 14:53
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srijatverma wrote:
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

(a) One
(b) Two
(c) Four
(d) Five
(e) Six


The number of 2-element subsets that can be formed from a 4-element set is 4C2 = (4 x 3)/2! = 6. Since the pair of elements 2 and 4 is only 1 of these 6 subsets, we have 6 - 1 = 5 subsets that do not contain the pair of elements.

Answer: D
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   07 Feb 2018, 12:41
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Hi All,

You can use the Combination Formula to answer this question, although we have to do a little bit of extra work at the end. Since the number of possible outcomes is so small, you could also list them all out.

4C2 = 4!/(2!2!) = 6 pairs

The pairs would be 12, 13, 14, 23, 24 and 34

Since we're asked to NOT use 24, there are 5 options remaining.

Final Answer:
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D


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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   24 Mar 2018, 11:03
srijatverma wrote:
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

(a) One
(b) Two
(c) Four
(d) Five
(e) Six


hi, :-)
can anyone explain what does subset mean ? I didn't understand the question ...
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   24 Mar 2018, 11:12
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dave13 wrote:
hi, :-)
can anyone explain what does subset mean ? I didn't understand the question ...


Hey dave13 ,

Subset means part of the set.

Here : Set is {1,2,3,4}

Subset could be {1} , {2}, {1,2},{1,2,3}, etc. where {1} is one element subset, {1,2} is two element subset and so on.

Question is asking how many such two element subsets could be made.

Does that make sense?
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   18 Sep 2021, 10:54
Correct option : 5 - D
Set {1,2,3,4}
Option : {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4} = 6
Not required : {2,4} = 1
Answer :6 - 1 = 5
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   18 Sep 2021, 11:14
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Asked: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

Total two-element subsets of {1,2,3,4} = 4C2 = 6 subsets
Subsets that contain the pair of elements 2 and 4 = {2,4} : 1 subset
Number of two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4 = 6-1 = 5

IMO D
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   26 Jan 2022, 14:27
Hey, so in case the question asks for 3 element we can choose it in 4C3 ways = 4 ways
So sets not having 2 and 4 will be 3

123
134
234 (this one will substract)
241

I hope my understanding is correct

Posted from my mobile device
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   26 Jan 2022, 22:36
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JenniferMassey wrote:
Hey, so in case the question asks for 3 element we can choose it in 4C3 ways = 4 ways
So sets not having 2 and 4 will be 3

123
134
234 (this one will substract)
241

I hope my understanding is correct

Posted from my mobile device


Hi JenniferMassey,

You are correct that there would be 4 possible groups of 3 elements. However, assuming that you want to remove any options that include BOTH a '2' and a '4', you would end up removing TWO of the four options (both 234 and 241).

GMAT assassins aren't born, they're made,
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Contact Rich at: Rich.C@empowergmat.com
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink] How many two-element subsets of {1, 2, 3, 4} are there that do not con   06 Dec 2023, 06:07
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Re: How many two-element subsets of {1, 2, 3, 4} are there that do not con [#permalink]
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