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For the equation `x + y + z +omega= 19,` the number of positive integral solutions is equal to-A. The number of ways `15` identical things can be distributed among `4` persons.B. The number of ways `19` identical things can be distributed among `4` persons.C. Coefficient of `x^(19)` in `(x^(0) + x^(1) + x^(2) + "………" + x^(19))^(4)`D. Coefficient of `x^(19)` in `(x + x^(2) + x^(3) + "………" + x^(19))^(4)` |
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Answer» Correct Answer - A::D Number of positive integral solution `= .^(19-1)C_(4-1) = .^(18)C_(3)` `=` Coefficients of `x^(19)` in `(x+x^(2)+x^(3)+"…….."+x^(19))^(4)` Number of ways in which `15` identical things can be distributed among `4` persons `= .^(15 + 4 -1)C_(15) = .^(18)C_(15) = .^(18)C_(3)` |
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