Find the number of solution of el + e2 + e3+e4 = 15, where el, e2, e3 and e4 are non- negative integers with 3 < el < 5, 4 < e2 < 6, 3 < e3 < 7, and 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the number of solution of el + e2 + e3+e4 = 15,
where e1, e2, e3 and e4 are non- negative integers
with 3 s el < 5, 4 < e2 < 6, 3 < e3 < 7, and 3se4<5?
I want the step of the answer like this example
Example 14
Find the number of solution of e, + e; + e, = 17, where e, ez and ez are non-
negative integers with 2 se, S 5, 3Se: 56, and 4se, S 7?
Solution:
The number of solutions with the indicated constraints is the coefficient
of x27 in the expansion of
+ x?)
(x² + x³ + x* + x$)(x³ + x+ + x³ + x°)(x+ +
(x5 + x6 + x + x® + x° + x
+ x° + x1° + x²"). (x* +
x + x + x' +
x')
= (x³ + 2x° + 3x7 + 4xº + 3x° + 2x1° + x+'). (x*
Transcribed Image Text:Find the number of solution of el + e2 + e3+e4 = 15, where e1, e2, e3 and e4 are non- negative integers with 3 s el < 5, 4 < e2 < 6, 3 < e3 < 7, and 3se4<5? I want the step of the answer like this example Example 14 Find the number of solution of e, + e; + e, = 17, where e, ez and ez are non- negative integers with 2 se, S 5, 3Se: 56, and 4se, S 7? Solution: The number of solutions with the indicated constraints is the coefficient of x27 in the expansion of + x?) (x² + x³ + x* + x$)(x³ + x+ + x³ + x°)(x+ + (x5 + x6 + x + x® + x° + x + x° + x1° + x²"). (x* + x + x + x' + x') = (x³ + 2x° + 3x7 + 4xº + 3x° + 2x1° + x+'). (x*
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