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Guichard-Combinatorics-Graph-Theory
· Problem 1.3.4
Fundamentals
Mathematics — Probability · binomial-coefficients
Problem
Use a combinatorial argument to prove that
(
k
2
)
+
(
n
−
k
2
)
+
k
(
n
−
k
)
=
(
n
2
)
\binom{k}{2} + \binom{n-k}{2} + k(n-k) = \binom{n}{2}
(
2
k
)
+
(
2
n
−
k
)
+
k
(
n
−
k
)
=
(
2
n
)
.
Related theory
General Term And Binomial Coefficients
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