Permutation Formula, QnA

Permutation
Sometimes the member of an event is the arrangement of a group of element which is taken from some elements which is provided. Suppose we want to determine the number of possible arrangements of the champion 1^st, 2^nd, 3^rd in a horse racing which is followed by 7 participants. To possible arrangement is surely different each other. The number of arrangements can be determined as the following.

All participants have possibility to the be 1^st champion, means there are 7 ways to determine the 1^st champion, then 6 participants is left to be the 2^nd champion, its means there are 6 ways to determine the 2^nd champion. If we have got the 1^st and 2^nd champion, then there ar 5 participants is left to be the 3^rd champion, its means there are 5 ways to determine the 3^rd champion. Based on the reduplication rule, then the possible arrangement that occupy the champion 1^st, 2^nd and 3^rd =7×6×5=210.

In determining the number of arrangements of champion position on the explanation above, we take 3 participants who will occupy the 1^st, 2^nd, and, 3^rd champion which are taken from 7 participants who follow the championship. The arrangement of the 1^st, 2^nd and 3^rd champion is called permutation. The number of possible arrangements is the number of permutation of the 3 objects which is taken from the 7 objects which are provided, and it is written by:
₇P₃ or P(7,3) or P_7,3 or P₃⁷
Pay attention that: P₃⁷=7∙6∙5, that can be changed into: