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Factorial, Biomial coefficient, and Pascal's triangle

The number $n!$, called $n$ factorial, is the product of $n$ with all of the positive integers less than $n$. The first few factorials areMATHThe binomial coefficient $\dbinom{n}{k}$, pronounced $n$ choose $k$, is the quotientMATHand counts the number of ways to pick $k$ things from $n$ things. The binomial coefficient gets it name from the fact thatMATHThe binomial coefficients can be generated using Pascal's triangleMATHwhere each row begins and ends with $1$, and each number in between is the sum of the two numbers above it.


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Historical sketch: Blaise Pascal

Table of power series: Binomial series


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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