例如:1, 2, 3, 4, 5这5个数字构成不同的5位数的总数为5! = 120
☆组合:COMBINATION
A PERMUTATION CAN BE THOUGHT OF AS A SELECTION PROCESS IN WHICH OBJECTS ARE SELECTED ONE BY ONE IN A CERTAIN ORDER. IF THESGROUPSOF SELECTION IS NOT RELEVANT AND ONLY K OBJECTS ARE TO BE SELECTED FROM A LARGER SET OF N OBJECTS, A DIFFERENT COUNTING METHOD IS EMPLOYED.
SPECIALLY CONSIDER A SET OF N OBJECTS FROM WHICH A COMPLETE SELECTION OF K OBJECTS IS TO BE MADE WITHOUT REGARD TO ORDER,SWHERES0≤K≤N . THEN THE NUMBER OF POSSIBLE COMPLETE SELECTIONS OF K OBJECTS IS CALLED THE NUMBER OF COMBINATIONS OF N OBJECTS TAKEN K AT A TIME AND IS CKN.
从N个元素中任选K个元素的数目为:
CKN. = N!/ (N-K)! K!
例如:从5个不同元素中任选2个的组合为C25 = 5!/2! 3!= 10
排列组合的一些特性(PROPERTIES OF PERMUTATION AND COMBINATION)
☆加法原则:RULE OF ADDITION
做某件事有X种方法,每种方法中又有各种不同的解决方法。例如第一种方法中有Y1种方法,第二种方法有Y2种方法,等等,第X种方法中又有YX种不同的方法,每一种均可完成这件事,即它们之间的关系用“OR”表达,那么一般使用加法原则,即有:Y1+ Y2+。。。+ YX种方法。
☆乘法原则:RULE OF MULTIPLICATION
完成一件事有X个步骤,第一步有Y1种方法,第二步有Y2种方法,。。。,第X步有YX种方法,完成这件事一共有Y1• Y2•。。。•YX种方法。
以上只是GMAT考题中经常涉及到的数学—算术方面的问题,今后我们将陆续在新开辟的“网上课堂”中介绍代数、几何以及系统的习题、讲解,以帮助大家在GMAT数学考试中更好地发挥中国学生的优势,拿到让美国人瞠目结舌的成绩!