From 41a2e0c7213c0ba708cd987ba164ea625dd6b21d Mon Sep 17 00:00:00 2001 From: Antti H S Laaksonen Date: Thu, 20 Apr 2017 23:20:52 +0300 Subject: [PATCH] Improve language --- chapter22.tex | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/chapter22.tex b/chapter22.tex index 676f857..a1b36af 100644 --- a/chapter22.tex +++ b/chapter22.tex @@ -112,8 +112,8 @@ Another way to calculate binomial coefficients is as follows: There are $n!$ permutations of $n$ elements. We go through all permutations and always -select the first $k$ elements of the permutation -to the subset. +include the first $k$ elements of the permutation +in the subset. Since the order of the elements in the subset and outside the subset does not matter, the result is divided by $k!$ and $(n-k)!$ @@ -124,10 +124,9 @@ For binomial coefficients, \[ {n \choose k} = {n \choose n-k}, \] -because we can either select $k$ -elements that belong to the subset -or $n-k$ elements that -do not belong to the subset. +because we actually divide a set of $n$ elements into +two subsets: the first contains $k$ elements +and the second contains $n-k$ elements. The sum of binomial coefficients is \[