In how many ways can 5 different books be arranged on a shelf? (2021)

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Question: In how many ways can 5 different books be arranged on a shelf? (2021)

Options:

Correct Answer: 720

Exam Year: 2021

Solution:

The number of arrangements of 5 distinct books is 5! = 120.

In how many ways can 5 different books be arranged on a shelf? (2021)

In how many ways can 5 different books be arranged on a shelf? (2021)

Step 1: Understand that we have 5 different books to arrange.
Step 2: Recognize 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 5 books, we calculate 5! which means 5 x 4 x 3 x 2 x 1.
Step 5: Perform the multiplication: 5 x 4 = 20, then 20 x 3 = 60, then 60 x 2 = 120, and finally 120 x 1 = 120.
Step 6: Conclude that there are 120 different ways to arrange the 5 books on the shelf.

Permutations – The arrangement of distinct objects in a specific order, calculated using factorial notation.