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# A math problem difficult.

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A math problem difficult. [#permalink]  24 Jul 2011, 03:50
How many two-element subsets of <1, 2,3,4> are there that do not contain the pair of elements 2 and 4?
a)1
b)2
c)4
d)5
e)6

I don't how to deal with it.
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Re: A math problem difficult. [#permalink]  24 Jul 2011, 06:19
tracyyahoo 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)1
b)2
c)4
d)5
e)6

I don't how to deal with it.

I also got it wrong first. But then the question says "do not contain the pair of elements [highlight]2 and 4[/highlight]

hence (1,2),(1,3), (1,4), (2,3),(3,4). Or 4C2 -1
Hence 5 sets.

Hence D
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Re: A math problem difficult. [#permalink]  08 Aug 2011, 08:39
You don't need to do any math for this. As soon as you see not including one element you know it will be odd (because you should know x2 will be somewhere in the way you solve it) and you can thus choose 5.
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Re: A math problem difficult. [#permalink]  08 Aug 2011, 09:23
tracyyahoo 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)1
b)2
c)4
d)5
e)6

I don't how to deal with it.

How many two-element subsets of <1, 2,3,4> are there - 4C2 = 4!/2! = 6
How many two-element subsets of 2-element sets that contain <2,4> = 2C2 = 2!/2! = 1

How many two-element subsets of <1, 2,3,4> are there that do not contain the pair of elements 2 and 4
= Number of two-element subsets of <1, 2,3,4> - two-element subsets of 2-element sets
= 6 - 1
= 5

You should know the Maths because the next time question may ask odd number of elements or the options will be different....

The pattern needs to be understood so that you can solve any future problem of the same type with different variants....

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From Jun 05, 2011 you have posted 146 posts and have not given a single Kudo !!!!!
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Re: A math problem difficult.   [#permalink] 08 Aug 2011, 09:23
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