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6
C_n^{2013} > C_a^{2013}, combinations (HOMC 2013 Q6)
C_n^{2013} > C_a^{2013}, combinations (HOMC 2013 Q6)
Source:
July 30, 2019
Combinations
inequalities
Problem Statement
Let be given
a
∈
{
0
,
1
,
2
,
3
,
.
.
.
,
100
}
.
a\in\{0,1,2, 3,..., 100\}.
a
∈
{
0
,
1
,
2
,
3
,
...
,
100
}
.
Find all
n
∈
{
1
,
2
,
3
,
.
.
.
,
2013
}
n \in\{1,2, 3,..., 2013\}
n
∈
{
1
,
2
,
3
,
...
,
2013
}
such that
C
n
2013
>
C
a
2013
C_n^{2013} > C_a^{2013}
C
n
2013
>
C
a
2013
, where
C
k
m
=
m
!
k
!
(
m
−
k
)
!
C_k^m=\frac{m!}{k!(m -k)!}
C
k
m
=
k
!
(
m
−
k
)!
m
!
.
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