For the equation x+y+z+w=19, the number of positive integral solutions is equal to

JEE Advanced Mathematics question

For the equation , the number of positive integral solutions is equal to

(A)the number of ways in which 15 identical things can be distributed among 4 personsCorrect
(B)the number of ways in which 19 identical things can be distributed among 4 persons
(C)coefficient of in
(D)coefficient of in Correct

Answer: (A),(D)

Solution

Positive solutions of : .

- **(a)** Distributing 15 identical things among 4 persons (some may get none) = non-negative solutions of . (Equivalently, put , etc.) Correct. - **(b)** 19 identical things among 4 persons: . Wrong. - **(c)**

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Question ID VK-108245