Find the number of ways in which India can win the series of 11 matches (If no match is drawn and all matches are played).

Answer

`2^(10)`

Explanation

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)`