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
Please help
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Hello,
This is how I could approach, I'll let the experts confirm if this approach is right..
Listing the combinations or using 4C2 to pick 2 out of 4,
12 21 31 41
13 23 32 42
14 24 34 43
and canceling out duplicates, we have 6 distinct values of which the only combination that has 2 and 4 is 24 removing which we have 5 values. So, I'll go with Option D
Thanks
Bullzi
This is how I could approach, I'll let the experts confirm if this approach is right..
Listing the combinations or using 4C2 to pick 2 out of 4,
12 21 31 41
13 23 32 42
14 24 34 43
and canceling out duplicates, we have 6 distinct values of which the only combination that has 2 and 4 is 24 removing which we have 5 values. So, I'll go with Option D
Thanks
Bullzi
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Hi Bullzi,
Your approach is great, although it has some redundant elements to it. If you're going to use the Combination Formula, then you don't have to list out all of the duplicate elements.
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.
GMAT assassins aren't born, they're made,
Rich
Your approach is great, although it has some redundant elements to it. If you're going to use the Combination Formula, then you don't have to list out all of the duplicate elements.
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.
GMAT assassins aren't born, they're made,
Rich
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Always check the answer choices before solving a math question on the GMAT.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
Given the very small answer choices, students should consider just listing all of the possible subsets.
They are:
(1,2)
(1,3)
(1,4)
(2,3)
(3,4)
The answer is D Five
Cheers,
Brent
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Listing and counting is often a useful approach on the GMAT. Here's a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... /video/773
Cheers,
Brent
Cheers,
Brent
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4C2 - 1 = 5 (D)oquiella 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