Daily Archives: February 17, 2012

二項式係數 3.1

Posted on by

Binomial coefficient 3.1

這段改編自 2010 年 5 月 25 日的對話。

nCr 的數值代表，如果要從 n 件物件中選 r 件出來，有多少個可能性。例如，從 5 個蘋果中，選 3 個出來的話，有多少種選擇呢？答案是 5C3，即是「5 選 3」，等於 10。

nCr 的另一個詮釋是，如果要把 n 件物件分成兩組，一組有 r 件，而另一組有 (n – r) 件的話，有多少個可能性。例如，假設要把 5 個蘋果分成兩袋。一袋有 3 個，而另一袋有 2 個。那樣，有多少個分配方法呢？答案是 5C3，即是「5 選 3」，等於 10。

只要你把 5C3 的公式寫出來，「分成兩組」的意思會格外明顯。　

5C3 =

(5!)
——–
(3!)(2!)

分子的「5!」代表總共有 5 個蘋果。分母有兩個因子，代表要分成兩袋。第一個因子是（3!)，代表第一袋要有 3 個蘋果。第二個因子是（2!)，代表第二袋要有兩個。

在這個 nCr 的詮釋下，「 nCr = nC(n-r) 」的原因一目了然。

— Me@2012.02.17

2012.02.17 Friday (c) All rights reserved by ACHK

Hacker News

Posted on by

Hacker News is a social news website about computer hacking and startup companies, run by Paul Graham’s funding firm Y Combinator. It is different from other social news websites in that there is no option to down vote submissions; submissions can either be voted up or not voted on at all. In contrast, comments can be down voted when a user accumulates sufficient “karma,” or points gained when submissions or comments are voted up. In general, content that can be submitted is defined as “anything that gratifies one’s intellectual curiosity”.

History

The site was created by Paul Graham in February 2007. Initially it was called Startup News or occasionally News.YC. On August 14, 2007 it became known by its current name. It developed as a project of his company Y Combinator, functioning as a real-world application of the Arc programming language which Graham co-developed.

The intention was to recreate a community similar to the early days of Reddit. Graham has stated he hopes to avoid the Eternal September that results in the general decline of intelligent discourse within a community.

— Wikipedia on Hacker News

2012.02.17 Friday ACHK