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combinatronics phrasing

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combinatronics phrasing [#permalink] New post 31 Oct 2011, 14:19
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?

OA= 105

What exactly do they mean by "different ways?" Isn't this question much different from:

"How many different groups can be made from a group of 8 people divided into 4 teams of 2 people each?"

which, wouldn't that be 8!/(6!2!) or 28.

I know no one is going to respond to this, but having done numerous questions of this type, I think this is a very important conceptual question. The way these questions are phrased can really have a profound effect.
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Re: combinatronics phrasing [#permalink] New post 31 Oct 2011, 23:32
The OA should be 105.

The number of ways of dividing 8 people into 4 teams of 2 each = 8!/[(2!^4) * 4!] = 105

8!/(6!2!) is the number of ways of dividing 8 people into two groups of 6 people and 2 people, which is wrong as the answer to the original question.
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Re: combinatronics phrasing   [#permalink] 31 Oct 2011, 23:32
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