InterviewSolution
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InterviewSolution
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Find the number of positive integral solutions satisfying the equation `(x_1+x_2+x_3)(y_1+y_2)=77.` |
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Answer» Correct Answer - 420 `(x_(1)+x_(2)+x_(3))(y_(1)+y_(2))=11xx7 " or " 7xx11` In the first case, `(x_(1)+x_(2)+x_(3))=11 " and" (y_(1)+y_(2))=7`, which have ` .^(10)C_(2). .^(6)C_(1)` solutions In the second case, `(x_(1)+x_(2)+x_(3))=7 " and" (y_(1)+y_(2))=11`, which have `.^(6)C_(2). .^(10)C_(1)` solutions `therefore` Total number of solutions `= .^(10)C_(2). .^(6)C_(1)+ .^(6)C_(2). .^(10)C_(1)` =270+150=420 |
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