Question: In how many ways can 5 books be arranged on a shelf?
Options:
120
60
24
30
Correct Answer: 120
Solution:
The number of ways to arrange 5 books is 5! = 120.
In how many ways can 5 books be arranged on a shelf?
Practice Questions
Q1
In how many ways can 5 books be arranged on a shelf?
120
60
24
30
Questions & Step-by-Step Solutions
In how many ways can 5 books be arranged on a shelf?
Correct Answer: 120
Step 1: Understand that arranging books means putting them in a specific order.
Step 2: Recognize that we have 5 different books to arrange.
Step 3: Realize that the first book can be any of the 5 books.
Step 4: After choosing the first book, there are 4 books left for the second position.
Step 5: For the third position, there are 3 books left to choose from.
Step 6: For the fourth position, there are 2 books left.
Step 7: Finally, for the last position, there is only 1 book left.
Step 8: Multiply the number of choices for each position: 5 × 4 × 3 × 2 × 1.
Step 9: Calculate the result: 5 × 4 = 20, then 20 × 3 = 60, then 60 × 2 = 120, and finally 120 × 1 = 120.
Step 10: Conclude that there are 120 different ways to arrange the 5 books.
Factorial – The concept of arranging distinct items is calculated using factorial notation, where n! (n factorial) represents the product of all positive integers up to n.
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