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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 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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New post 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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New post 15 Sep 2017, 02:38
Why we should not delete 2, one for (4,2) also

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New post 15 Sep 2017, 02:46
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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How many two-element subsets of {1,2,3,4} are there that do not [#permalink]

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New post 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.

Answer D

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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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New post 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.

Answer: D
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Re: How many two-element subsets of {1,2,3,4} are there that do not   [#permalink] 21 Sep 2017, 14:53
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