Date: Feb 5, 2013 10:02 AM
Author: fom
Subject: Re: how many ways to pick two teams

On 2/5/2013 3:02 AM, quasi wrote:
> fom wrote:
>> William Elliot wrote:
>>> G Patel wrote:
>>>

>>>> Is it 20 choose 10 or do I have to divide by 2?
>>>>

>>> What's it?
>>
>> What do you mean by picking teams? Combinations are without
>> regard to order,
>>
>> captains will try to make the best pick at each opportunity
>> to choose...
>>
>> 20*18*16*14*12*10*8*6*4*2
>>
>> 19*17*15*13*11*9*7*5*3*1

>
> In the context of this problem, the only interest is in
> determining the number of possible results for the two teams,
> not in the mechanism by which the selection was performed.
>
> In particular, the order of selecting people doesn't matter.
>
> The intent of the problem is to find the number of possible
> partitions of a 20-element subset into two 10-element subsets.


The intent of the question was to ask how to solve
a combination. The stated problem was how to
choose teams. Any kid who grew up playing sandlot
baseball knows the rules that formed the basis
of my remark. And, order does matter. The kids
who are picked last are painfully aware of their
status.

While I agree with you concerning the original
poster's interest (and sadly had not thought
that far before my own post), it may well be
that they would have been helped by
my observation under slightly different
circumstances. That is, they might have
had a need to at least consider the problem
differently.

Thank you, though. I am so out of practice
that I find the assistance you give to
others quite interesting, even if it is
sometimes trivial to you.