Question
Question: The number of positive integral solution of 2x<sub>1</sub> + 3x<sub>2</sub> + 4x<sub>3</sub> + 5x<s...
The number of positive integral solution of
2x1 + 3x2 + 4x3 + 5x4 = 25 is -]
A
20
B
22
C
23
D
None of these
Answer
None of these
Explanation
Solution
The number of required solutions
= Coefficient of y25 is (y2 + y4 + y6 + ….)
(y3 + y6 + y9 + …..) (y4 + y8 + y12 + ….)
y5 + y10 + y15 + ….)
= Coefficient of y25 is y14 [(1 + y2 + y4 + y6 + y8)
(1 + y3 + y6 + y9)]
[(1 + y4 + y8 +…) (1 + y5 + y10 +….)]
= Coefficient of y11 is (1 + y2 + y3 + y4 + y5 + y6
+ y7 + 2y8 + 2y9 + 2y10 + 2y11 + ...)
(1 + y4 + y5 + y9 + y10 + y13 + ….)= 2 + 1 + 1 + 1 = 5.