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How many ways can you arrange 5 books on a shelf?

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Question: How many ways can you arrange 5 books on a shelf?

Options:

  1. 120
  2. 60
  3. 24
  4. 30

Correct Answer: 120

Solution: 

The number of arrangements of 5 books is 5! = 5 × 4 × 3 × 2 × 1 = 120.

How many ways can you arrange 5 books on a shelf?

Practice Questions

Q1
How many ways can you arrange 5 books on a shelf?
  1. 120
  2. 60
  3. 24
  4. 30

Questions & Step-by-Step Solutions

How many ways can you arrange 5 books on a shelf?
  • Step 1: Understand that arranging books means putting them in a specific order.
  • Step 2: Realize that you have 5 different books to arrange.
  • Step 3: The first book can be any of the 5 books.
  • Step 4: After choosing the first book, you have 4 books left to choose from for the second position.
  • Step 5: For the third position, you will have 3 books left to choose from.
  • Step 6: For the fourth position, you will have 2 books left.
  • Step 7: Finally, for the last position, you will have only 1 book left.
  • Step 8: To find the total number of arrangements, multiply the number of choices for each position: 5 × 4 × 3 × 2 × 1.
  • Step 9: Calculate the multiplication: 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 on the shelf.
  • Factorial – The concept of factorial (n!) is used to determine the number of ways to arrange n distinct objects.
  • Permutations – This question tests the understanding of permutations, specifically how to calculate the total arrangements of a set of items.
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