(3) (i) Determine the number of positive solutions of the equation x1+x2+x3+X4 = 14, where each x; cannot exceed 8, for 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(3) (i) Determine the number of positive solutions of the equation x1+x2+X3+x4 =
14, where each x; cannot exceed 8, for 1 < i < 4.
(ii)) Determine the number of integral solutions of the equation x1+x2+x3+X4 =
20, where 1 < x1 < 6, 0 < x2 < 7, 4 < x3 < 8, and 2 < x4 < 6.
Transcribed Image Text:(3) (i) Determine the number of positive solutions of the equation x1+x2+X3+x4 = 14, where each x; cannot exceed 8, for 1 < i < 4. (ii)) Determine the number of integral solutions of the equation x1+x2+x3+X4 = 20, where 1 < x1 < 6, 0 < x2 < 7, 4 < x3 < 8, and 2 < x4 < 6.
(2) Let S := {1, ..., n}. Compute the number of towers of length of the form
Aj c A2 c S, where A1 + Ø, A + A2, and A2 + S.
Transcribed Image Text:(2) Let S := {1, ..., n}. Compute the number of towers of length of the form Aj c A2 c S, where A1 + Ø, A + A2, and A2 + S.
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