数学机经请教

lkmxy1988212

264:Jane (人名是我随便编的) is to pay 5 bills, and the 5 bills are with different amounts. If Jane is to pay the greatest amount bill first and the least amount bill last... what is the possibility she has?答案都是分数。。。
3！/ 5! = 1/20
有谁能给解释一下这个式子是怎么得出来的吗？

sdcar2010

5 random: 5!

Greatest M M M Least : 3!

gkast

我会避免用combination。

第一个bill 只有一个可能: greatest amount bill = 1/5
第二个bill 剩4个bill 情况下，选3个非least amount bill = 3/4
第三个bill 剩3个bill 情况下，选2个非least amount bill = 2/3
第四个bill 剩2个bill 情况下，只能选非least amount bill = 1/2
第五个bill 没的选，就 1

all cases dependent，用乘 (independent cases 用加):
1/5 * 3/4 * 2/3 * 1/2 * 1 = 1/20