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In how many ways can 30 marks be allotted to 8 questionif each question carries at least 2 marks?A. `""^(21)C_(7)`B. `""^(21)C_(8)`C. `""^(21)C_(9)`D. none of these

Answer» Let `x_(1)` denote the marks assigned to the ith question. Then,
`x_(1)+x_(2)+x_(3)+x_(4)+x_(5)+x_(6)+x_(7)+x_(8)=30`
where `x_(1)ge2,i=1,2,....,8`.
Let, `y_(i)=x_(i)-2,i=1,2,....8`. Then,
`x_(1)+x_(2)+x_(3)+....x_(8)=30`
`impliesy_(1)+y_(2)+y_(3)+......+y_(8)=14`
The total number of solutions of this equation is
`""^(14+8-1)C_(8-1)=""^(21)C_(7)`.


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