Posted by Sarah on Monday, November 4, 2013 at 4:46am.
How many ways can you arrange the order of 4articles on a shelf?please explain why it is 4 x3x2x1,thanks

Math  Reiny, Monday, November 4, 2013 at 9:18am
Think of it as 4 spots to fill
 you can fill the first spot with 4 different books
 that leaves you with 3 books to place, and the 2nd spot can be filled with any of those 3 remaining books.
 leaving you with 2 books, so the third spot can be filled with either of those 2 books
 which leaves you with 1 book to place in the last spot
Now, it becomes a multiplication, since for each of the first 4 placements I can repeat the last 3 routines, etc
no it becomes 4x3x2x1 or 4! or 24
reduce the problem to 3 books , and we list them.
books A, B, C
ABC  ACB
BAC  BCA
CAB  CBA > There are 6 of these, or 3x2x1
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