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

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Intern
Joined: 07 Sep 2016
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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, 02:55
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54% (01:04) correct 46% (01:05) wrong based on 377 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

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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, 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: $$C^2_4-1=5$$.

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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, 23:07
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, 23:23
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1
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, 02:38
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, 02:46
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, 12:00
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, 14:53
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]

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07 Feb 2018, 12:41
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.

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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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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  [#permalink]

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24 Mar 2018, 11:12
1
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 &nbs [#permalink] 24 Mar 2018, 11:12
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