Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 121

Suppose that we have n distinct objects . We can determine how many different sequences of x objects can be formed by choosing x objects in succession from the n objects where . For convenience, we may think of a sequence of x places that are to be filled with x objects. We have n choices of objects to fill the first place. After the first place is filled, then with objects left, we have choices to fill the second place. Each of the n choices for filling the first place can be combined with each of the choices for filling the second place, thus yielding ways of filling the first two places. By continuing this argument, we will see that there are ways of filling the x places by choosing x objects from the set of n objects. Each of these sequences or arrangements of x objects is called a permutation of x objects from n. The total number of permutations of x objects from n, denoted by , is given by

(3.4.1)

Note that the number of ways of permuting all the objects is given by

(3.4.2)

where is read as n factorial.

Expressed in terms of factorials, we easily find that

(3.4.3)