The number of all subsets of a set containing `2n+1` elements which contains more than `n` elements is

Options

A. `2^(n)`
B. `2^(2n)`
C. `2^(n+1)`
D. `2^(2n-1)`

Answer

B

Explanation

`.^(2n+1)C_(n+1)+ .^(2n+1)C_(n+2)+…+ .^(2n+1)C_(2n+1)`
`=1/2((.^2n+1)C_(0)+ .^(2n+1)C_(1)+ .^(2n+1)C_(3)+…+ .^(2n+1)C_(2n+1))=2 .^(2n)`