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How Many 2 Elemen Subsets of.....

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by pakaskwa » Sat Apr 25, 2009 2:06 pm
IMO it's B.

To pick out any 2 items out of 3 items, there are 2C3 possible ways.

To pick out 2 selected items out of 3 items, there are 2C2 possible ways.

Therefore, to pick out any 2 items out of 3 items, but NOT including those 2 selected items are:
2C3-2C2=3-1=2
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by mkbigmoz » Sat Apr 25, 2009 2:34 pm
[spoiler]The answer is 2, but I didnt use your formula. I wrote out the possibilities and came up with 4 (7-8, 8-9, 8-7, 9-8). Obviously my answer was wrong, but could you explain why I cant reverse the integers?[/spoiler]
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by pakaskwa » Sat Apr 25, 2009 2:43 pm
1st, we need to determine if it's a "combination" or "permutation" question. In the question stem, it says "pair of elements 7 and 9". A pair means "7,9" and "9,7" are the same. So it's a combination issue. The order of 7 and 9 doesn't matter.

2nd, it's always better to know both (or more) methods to solve the same problem. When the set is getting too big and you can't write all possible subsets, you can use formula.

For example, let's change the question to:
How many three-element subsets of {2,3,4,5,6,7,8,9,10} do NOT contain 3-element set {7,8,9}?

It would be impossible to write all subsets within 2 minutes. But you can easily get the answer by using formula: 3C10-3C3=119.
Last edited by pakaskwa on Sun Apr 26, 2009 11:14 pm, edited 1 time in total.
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by Vemuri » Sun Apr 26, 2009 8:04 pm
pakaskwa wrote: It would be impossible to write all subsets within 2 minutes. But you can easily get the answer by using formula: 3C10-3C3=239.
Hi pakaskwa,

I hope you meant 10c3-3c3 = 120-1=119 in the above example.
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by pakaskwa » Sun Apr 26, 2009 11:13 pm
You are right Vemuri. I was not careful. It should be 119. I'll edit on my posting and not to mislead people.

Thanks!
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by Ian Stewart » Mon Apr 27, 2009 5:36 am
mkbigmoz wrote:The answer is 2, but I didnt use your formula. I wrote out the possibilities and came up with 4 (7-8, 8-9, 8-7, 9-8). Obviously my answer was wrong, but could you explain why I cant reverse the integers?
In a set (or in a subset), the order of the elements is not important. So, the set {1, 3, 5} is the same set as {3, 1, 5}, or {5, 1, 3}, etc. Since this question asks how many subsets we can choose, the order is not important, and {7, 8} should be considered to be the same as {8, 7} (and this is the reason it's a 'combinations question', and not a 'permutations question').

Since the answer here is just two, writing out all of the possibilities is a perfectly good approach - {7, 8} and {8, 9} are the only answers - though if the question featured a larger set, the approach would not be practical.

That said, while I could imagine this kind of question appearing on a GMAT, I don't believe I've ever seen a real GMAT question that tested counting with this setup (choosing subsets from a set), so understanding this particular question isn't likely to be important on test day.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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