Correct Answer - `2^(10)`
India must win at least 6 matches of 11 matches.
Then number of ways in which Indain can win the series
`= .^(11)C_(6)+ .^(11)C_(7)+..+ .^(11)C_(11)`
Now ` .(11)C_(0)+ .^(11)C_(1)+ .^(11)C_(2)+..+ .^(11)C_(10) + .^(11)C_(11)=2^(11)`
`implies 2(.^(11)C_(6)+ .^(11)C_(7)+..+ .^(11)C_(11))=2^(11) " "("Using" .^(n)C_(r )= .^(n)C_(n-r))`
`therefore .^(11)C_(6)+ .^(11)C_(7)+..+ .^(11)C_(11)=2^(10)`