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Find the number of positive integral sol...

Find the number of positive integral solutions satisfying the equation `(x_1+x_2+x_3)(y_1+y_2)=77.`

Text Solution

Verified by Experts

The correct Answer is:
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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