Formelblad
Matematik 1
Matematik 2
Matematik 3
Matematik 4
Matematik 5
Matematik 1
Matematik 2
Matematik 3
Matematik 4
Matematik 5
1
Ma1
2
Ma2
3
Ma3
4
Ma4
5
Ma5
Hem
Kombinatorik
Kombinatorik
Formler från Matematik 5
Kombinatorik
Ma5
Permutationer
P
(
n
,
k
)
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋅
.
.
.
⋅
(
n
−
k
+
1
)
=
n
!
(
n
−
k
)
!
P(n,k) = n \cdot (n-1) \cdot (n-2) \cdot ... \cdot (n-k+1) = \frac{n!}{(n-k)!}
P
(
n
,
k
)
=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋅
...
⋅
(
n
−
k
+
1
)
=
(
n
−
k
)!
n
!
0 ≤ k ≤ n
Ma5
Kombinationer
C
(
n
,
k
)
=
(
n
k
)
=
P
(
n
,
k
)
k
!
=
n
!
k
!
(
n
−
k
)
!
C(n,k) = \binom{n}{k} = \frac{P(n,k)}{k!} = \frac{n!}{k!(n-k)!}
C
(
n
,
k
)
=
(
k
n
)
=
k
!
P
(
n
,
k
)
=
k
!
(
n
−
k
)!
n
!
0 ≤ k ≤ n
Ma5
Binomialsatsen
(
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