☆排列：permutations

　　The factorial is useful for counting the number of ways that a set of objects can be ordered. If a set of n objects is to be ordered from 1st to nth, there are n choices for the 1st object, n-1 choices for the 2nd object, n-2 choices for the 3rd object, and so on, until there is only 1 choice for the nth object. Thus, by the multiplication principle, the number of ways of ordering the n objects is

　　　　　　　　　　n (n-1) (n-2)…( 3) (2) (1) = n!

　　For example, the number of ways of ordering the letters A, B, and C is 3!, or 6：ABC, ACB, BAC, BCA, CAB, and CBA.

　　These orderings are called the permutations of the letters A, B, and C.也可以用P 33表示.

　　　　　　　　　　　　　　　　　　　　　　　　　　Pkn = n!/ (n-k)!

　　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 the order of 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, where 0≤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！