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Find the number of ways in which India c...

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).

Text Solution

Verified by Experts

The correct Answer is:
`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)`
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