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

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How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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01 Nov 2016, 01:55
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53% (00:44) correct 47% (00:43) wrong based on 227 sessions

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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
[Reveal] Spoiler: OA

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Srijat Verma
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Appearing for GMAT in 2016

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Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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01 Nov 2016, 03:04
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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: $$C^2_4-1=5$$.

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Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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14 Sep 2017, 22:07
Bunuel,
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 [#permalink]

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14 Sep 2017, 22:23
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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 [#permalink]

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15 Sep 2017, 01:38
Why we should not delete 2, one for (4,2) also

Sent from my XT1045 using GMAT Club Forum mobile app
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Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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15 Sep 2017, 01:46
vs224 wrote:
Why we should not delete 2, one for (4,2) also

Sent from my XT1045 using GMAT Club Forum mobile app

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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How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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15 Sep 2017, 11:00
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.

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Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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21 Sep 2017, 13:53
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.

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Re: How many two-element subsets of {1,2,3,4} are there that do not   [#permalink] 21 Sep 2017, 13:53
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