How many ways can 6 different books be arranged on a shelf? (2017)

How many ways can 6 different books be arranged on a shelf? (2017)

Step 1: Understand that we have 6 different books to arrange.
Step 2: Realize that the order in which we arrange the books matters.
Step 3: Use the factorial notation to calculate the number of arrangements. The factorial of a number n (written as n!) is the product of all positive integers up to n.
Step 4: For 6 books, we calculate 6! which means 6 x 5 x 4 x 3 x 2 x 1.
Step 5: Perform the multiplication: 6 x 5 = 30, then 30 x 4 = 120, then 120 x 3 = 360, then 360 x 2 = 720, and finally 720 x 1 = 720.
Step 6: Conclude that there are 720 different ways to arrange the 6 books on the shelf.

Permutations – The arrangement of a set of distinct items where the order matters, calculated using factorial notation.