In how many ways can 5 different books be arranged on a shelf? (2021)
Practice Questions
1 question
Q1
In how many ways can 5 different books be arranged on a shelf? (2021)
60
120
240
720
The number of arrangements of 5 distinct books is 5! = 120.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 5 different books be arranged on a shelf? (2021)
Solution: The number of arrangements of 5 distinct books is 5! = 120.
Steps: 6
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.
