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Combinatorics
5 formulas · Mathematics
Permutations
P
n
=
n
!
P_n=n!
P
n
=
n
!
Variations without repetition
V
n
k
=
n
!
(
n
−
k
)
!
V_n^k=\dfrac{n!}{(n-k)!}
V
n
k
=
(
n
−
k
)!
n
!
Variations with repetition
V
‾
n
k
=
n
k
\overline{V}_n^k=n^k
V
n
k
=
n
k
Combinations (binomial coefficient)
(
n
k
)
=
n
!
k
!
(
n
−
k
)
!
\binom{n}{k}=\dfrac{n!}{k!(n-k)!}
(
k
n
)
=
k
!
(
n
−
k
)!
n
!
Binomial theorem
(
a
+
b
)
n
=
∑
k
=
0
n
(
n
k
)
a
n
−
k
b
k
(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k}
(
a
+
b
)
n
=
k
=
0
∑
n
(
k
n
)
a
n
−
k
b
k
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