upload diverse filer

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2025-12-10 13:13:05 +01:00
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@@ -5,7 +5,7 @@ Section 6.4
= Binomial coefficient
From last week:
$C(n, k) = $ the number of k-combinations from an n-set. Or the number of ways to select k elements from an n-set. Or the number of k-subsets of an n-set. Formula: $n!/(k!-(n-k)!)=mat(n;k)$ for $0<=k<=n$
$C(n, k) = $ the number of k-combinations from an n-set. Or the number of ways to select k elements from an n-set. Or the number of k-subsets of an n-set. Formula: $n!/(k!(n-k)!)=mat(n;k)$ for $0<=k<=n$
== Pascal's triangle
@@ -175,4 +175,4 @@ $ (x+y)¹&=mat(1;0)dot x⁰ dot y¹ + mat(1;1)dot x¹ dot y⁰\
Therefore, the coefficient of $x^(n-k)y^k$ is $binom(n,k)$.
= Van der Mande
$mat(m+n;r)=sum^r_(k=0)mat(m;r-k) mat(n;k)$
$mat(m+n;r)=sum^r_(k=0)mat(m;r-k) mat(n;k)$