In how many ways can 4 different books be arranged on a shelf?

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Question: In how many ways can 4 different books be arranged on a shelf?

Options:

Correct Answer: 24

Solution:

The number of arrangements of 4 different books is 4! = 24.

In how many ways can 4 different books be arranged on a shelf?

In how many ways can 4 different books be arranged on a shelf?

Step 1: Understand that we have 4 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 4 books, we calculate 4! which means 4 x 3 x 2 x 1.
Step 5: Perform the multiplication: 4 x 3 = 12, then 12 x 2 = 24, and finally 24 x 1 = 24.
Step 6: Conclude that there are 24 different ways to arrange the 4 books on the shelf.

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