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Guichard-Combinatorics-Graph-Theory
· Problem 1.3.14
Fundamentals
Mathematics — Probability · binomial-coefficients
Problem
Give a combinatorial proof of
∑
i
=
0
k
(
m
i
)
(
n
k
−
i
)
=
(
m
+
n
k
)
.
\sum_{i=0}^{k} \binom{m}{i}\binom{n}{k-i} = \binom{m+n}{k}.
i
=
0
∑
k
(
i
m
)
(
k
−
i
n
)
=
(
k
m
+
n
)
.
Rewrite this identity in simpler form if
m
=
n
m = n
m
=
n
, and when
k
=
m
=
n
k = m = n
k
=
m
=
n
.
Related theory
General Term And Binomial Coefficients
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