Question 702762: I have seven books. How many different orders can I read the books in? Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! I have seven books. How many different orders can I read the books in?
-----------------
The 1st choice is 1 of 7.
Then 1 of 6, etc
--> 7*6*5*4*3*2*1
= 7!
= 5040 ways
You can choose the book to read 1st in 7 ways.
Having chosen the first book to read, there are 6 books
left to choose to read 2nd. So there are 7×6 ways
to choose to read the first 2 books.
Having chosen the first 2 books to read, there are 5 books
left to choose to read 3rd. So there are 7×6×5 ways
to choose to read the first 3 books.
Having chosen the first 3 books to read, there are 4 books
left to choose to read 4th. So there are 7×6×5×4 ways
to choose to read the first 4 books.
Having chosen the first 4 books to read, there are 3 books
left to choose to read 5th. So there are 7×6×5×4×3 ways
to choose to read the first 5 books.
Having chosen the first 5 books to read, there are 2 books
left to choose to read 6th. So there are 7×6×5×4×3×2 ways
to choose to read the first 6 books.
Having chosen the first 6 books to read, there is only 1 book
left to read 7th. So there are 7×6×5×4×3×2×1 ways
to choose to read all 7 books.
Answer: 7×6×5×4×3×2×1 = 7! = 5040 different orders.
Edwin
