Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Prove that
m
+
n
C
r
=
m
C
r
+
m
C
r
−
1
n
C
1
+
m
C
r
−
2
n
C
2
+
⋯
+
n
C
r
{}^{m+n} C_r = {}^m C_r + {}^m C_{r-1} {}^n C_1 + {}^m C_{r-2} {}^n C_2 + \dots + {}^n C_r
m
+
n
C
r
=
m
C
r
+
m
C
r
−
1
n
C
1
+
m
C
r
−
2
n
C
2
+
⋯
+
n
C
r
If
r
<
m
,
r
<
n
r < m, r < n
r
<
m
,
r
<
n
and
m
,
n
,
r
m, n, r
m
,
n
,
r
are positive integers.
Browse the problem library