Set Theory Doubt

Question

 

Approach : 1.

Select given number say 1,  then find combination of rest of the elements. 

e.g  select 1 , now remaining 4 elements, make subsets of 2 elements and add "1" in each subsets  ie  C(4,2) = 6. 

Suggest any another method please.

 

Comments

We want to find in how many subset of size $m$ of $n$ elements the element $x$ is present.

for every size $m$, one element is fixed $i.e.$ x , so we have $m-1$ spaces to fill and $n-1$ elements left, so, the sets would be ${}^{n-1}C_{m-1}$

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@Shobhit Joshi 

the same i explained as Approach 1. 

I need some other method if any.

( Please read the question along with explanation given under question )

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@HeadShot my bad.