In how many ways can 6 different books be arranged on a shelf?

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Question: In how many ways can 6 different books be arranged on a shelf?

Options:

Correct Answer: 720

Solution:

The number of arrangements of 6 different books is 6! = 720.

In how many ways can 6 different books be arranged on a shelf?

In how many ways can 6 different books be arranged on a shelf?

Step 1: Understand that we have 6 different books to arrange.
Step 2: Realize that the arrangement of books is a permutation problem, where the order matters.
Step 3: Use the factorial notation to represent the number of ways to arrange the books. The factorial of a number n (written as n!) is the product of all positive integers up to n.
Step 4: Calculate 6! (6 factorial). This means you multiply 6 by every whole number less than it down to 1: 6 × 5 × 4 × 3 × 2 × 1.
Step 5: Perform the multiplication: 6 × 5 = 30, then 30 × 4 = 120, then 120 × 3 = 360, then 360 × 2 = 720, and finally 720 × 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 items where the order matters, calculated using factorial notation.