et n > 3 and 2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 29EQ
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Let n > 3 and 2 < k < n – 1. Prove the inequality
(;) - (*- **) > (;)
')<(3)
k
n – k +
+
in two ways: (a) algebraic proof, and (b) combinatorial proof
Hint for (b): show that the left side counts only some of the things counted by the right side.
Transcribed Image Text:Let n > 3 and 2 < k < n – 1. Prove the inequality (;) - (*- **) > (;) ')<(3) k n – k + + in two ways: (a) algebraic proof, and (b) combinatorial proof Hint for (b): show that the left side counts only some of the things counted by the right side.
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