1. subset 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???

2. Originally Posted by tukilala
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???
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.

3. 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

4. Originally Posted by tukilala
i ment how many sets with length=10 exist in {1,2,3,....,100}
That is a simple combination question: $\displaystyle {{100}\choose{10}}=\frac{100!}{(10!)(90!)}$

5. 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

6. Originally Posted by tukilala
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????
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