A⊂(1,2,3......100) |A|=10

how many subsets posibilities exist that A will be a subset.

i know the answers is 2^10, but why????

if A⊂(1,2,3......200) |A|=10, so the number of posebilitis of A been a subset is still 2^10??? why? and how???

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- Jan 23rd 2009, 09:32 AMtukilalasubset question
A⊂(1,2,3......100) |A|=10

how many subsets posibilities exist that A will be a subset.

i know the answers is 2^10, but why????

if A⊂(1,2,3......200) |A|=10, so the number of posebilitis of A been a subset is still 2^10??? why? and how??? - Jan 23rd 2009, 10:31 AMPlato
There are indeed

**$\displaystyle 2^{10}$ subsets of A**.

**BUT, that is not the way you have worded the question.**

You have ask “how many subsets of {1,2,3,…,100} are**supersets of A**?”

That is how many subsets of {1,2,3,…,100} have A as a subset.

The answer to that is $\displaystyle 2^{90}$. So which is your question?

Is it about subsets of A? Or is it about supersets of A?

There is no point in my guessing which question you need help with. - Jan 23rd 2009, 11:05 AMtukilala
i ment how many sets with length=10 exist in {1,2,3,....,100}

for example: (1,2,3,4,5,6,7,8,9,10),(1,2,3,4,5,6,7,8,9,11),(1,1 0,20,30,40,50,60,70,80,90,100),(91,92,93,94,95,96, 97,98,99,100) ,.................................

so how many? and how are you get to the answer???

thanks - Jan 23rd 2009, 11:08 AMPlato
- Jan 23rd 2009, 04:35 PMtukilala
ok,

so i want to pick 10 elements of the initial set, which contains 100 elements

i know that the answer sepose to be 2^10, but why???? i dont understand...

if i want to pick 10 elements of the initial set, which contains 200 elements, so how many sub set will be now? still 2^10?? if yes, why?

if not so how many? and why?

thnx - Jan 24th 2009, 03:24 AMPlato
**That statement is simply wrong!**

There are $\displaystyle \frac{100!}{(90!)(10!)}$ ways to pick 10 elements from a set of 100.

Why do you think there are only $\displaystyle 2^{10}$? That is the number of subsets in a set of 10.

There are $\displaystyle \frac{200!}{(190!)(10!)}$ ways to pick 10 elements from a set of 200.

There are $\displaystyle \frac{300!}{(290!)(10!)}$ ways to pick 10 elements from a set of 300.

etc