Java源码——使用BigInteger计算组合数（彩票中奖概率计算示例）

1. 问题描述

双色球中，红色球选号规则：红色球可以在1-33个编号中任意选择6个。

问题：红色球全部选中的概率为多少？

2. 代码：

package v1ch03.BigIntegerTest;import java.math.*;
import java.util.*;/*** This program uses big numbers to compute the odds of winning the grand prize in a lottery.* @version 1.20 2004-02-10* @author Cay Horstmann*/
public class BigIntegerTest
{public static void main(String[] args){Scanner in = new Scanner(System.in);System.out.print("How many numbers do you need to draw? ");int k = in.nextInt();System.out.print("What is the highest number you can draw? ");int n = in.nextInt();/** compute binomial coefficient n*(n-1)*(n-2)*...*(n-k+1)/(1*2*3*...*k)*/BigInteger lotteryOdds = BigInteger.valueOf(1);for (int i = 1; i <= k; i++)lotteryOdds = lotteryOdds.multiply(BigInteger.valueOf(n - i + 1)).divide(BigInteger.valueOf(i));System.out.println("Your odds are 1 in " + lotteryOdds + ". Good luck!");}
}

运行结果：

How many numbers do you need to draw? 6
What is the highest number you can draw? 33
Your odds are 1 in 1107568. Good luck!

即，红色球全部选中的概率为：1107568分之一（约111万分之一）。

另外，本程序也可以演示BigInterger类的强大之处，如下所示：

How many numbers do you need to draw? 500
What is the highest number you can draw? 5000
Your odds are 1 in 152383570502276241773112299038287011759805517717774989612063963324852197721349960590884233711082048864016759544054508257767390473359453022881045964121514812790325726285875069528156914452728158646183348385785484897051302963702456469661925649013938025675652103406710218905355077057732196294852278472953496440392540565238652496586095257231832780763525058654245376714838913660805861811146730935555609878975704618923988507281746376470494321008996284739018893410735106722857930028973378877130054931747509530956061693359470175950233574962808714004842287921921934995121777448532875190191549476629085646880295182806621692835943142454947817131669088583382928050125741393952210717943794438066831202814961683139272640. Good luck!

若在Excel中使用Combin()函数来计算，Combin(5000,500)，将会发现溢出错误（#NUM)。而本程序的计算结果为705位数之多。至于最高支持多少位的计算，暂不深究，够用就行。