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# DM - Grand Test -Q13

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+1 vote

Let S be a set of 12 elements. Let a, b be two different specific elements of S i.e. a,b $\dpi{100} \in$ S and let $\dpi{100} 2^S$ denote the set of all subsets of set S. Then $\dpi{100} |\{x:x\in 2^S \text{ and } a,b \in x\}|$ is ________?

reshown Aug 31, 2020

+1 vote

Since a and b are specific two different elements, so,  $\dpi{100} |\{x:x\in 2^S \text{ and } a,b \in x\}|$  means the number of subset of S which contain both a,b. So, a,b must be in the subset, and remaining 10 elements have choice of being in or not in the subset, so, we have  2^10 such subsets.