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

Question

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

Bunuel · Accepted Answer

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

Or:  C^2_4-1=5 .

Answer: D.

Bunuel · Answer

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.

e100 · Answer

Bunuel , 
Could you please explain why do you deduct one?

Bunuel · Answer

4C2 is the number of ALL two-element subsets. We subtract one subset {2, 4} to get the desired number.

generis · Answer

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

ScottTargetTestPrep · Answer

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

Answer: D

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

dave13 · Answer

hi,

can anyone explain what does subset mean ? I didn't understand the question ...

abhimahna · Answer

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?

100mitra · Answer

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

Kinshook · Answer

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

JenniferMassey · Answer

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

EMPOWERgmatRichC · Answer

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, Rich Contact Rich at: Rich.C@empowergmat.com

kashisshhhhh · Answer

Hi,

but the question says 2and 4, not 2 or 4. That would only one be one case for 2 and 4.

Bunuel · Answer

It means you only exclude the specific pair {2,4}, not all subsets containing 2 or 4 separately. So every pair is allowed except {2,4}, which leaves 5 valid subsets.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards