Question

A set contains $4n+1$ elements.The number of subsets of this set containing more than $2n$ elements

• A. $2^{2n-1}$
• B. $2^{2n}$
• C. $2^{2n+1}$
• D. $2^{4n}$

Answer 1

The correct option is D $2^{4n}$

The number of sub sets containing $n$ elements $=2^{n+1}$

Given the set contains $4n+1$ elements

Number of subsets with element more than $2n$

$={\left(2\right)}^{4n}$

Hence the correct answer is ${\left(2\right)}^{4n}$