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How many ways can 5 different books be arranged on a shelf?

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Question: How many ways can 5 different books be arranged on a shelf?

Options:

  1. 60
  2. 120
  3. 100
  4. 80

Correct Answer: 120

Solution: 

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

How many ways can 5 different books be arranged on a shelf?

Practice Questions

Q1
How many ways can 5 different books be arranged on a shelf?
  1. 60
  2. 120
  3. 100
  4. 80

Questions & Step-by-Step Solutions

How many ways can 5 different books be arranged on a shelf?
Correct Answer: 120
  • Step 1: Understand that we have 5 different books to arrange.
  • Step 2: Realize that the order in which we arrange the books matters.
  • Step 3: Use the factorial notation, which is represented by 'n!'. This means we multiply all whole numbers from n down to 1.
  • Step 4: For 5 books, we calculate 5! (5 factorial).
  • Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1.
  • Step 6: Perform the multiplication: 5 × 4 = 20, then 20 × 3 = 60, then 60 × 2 = 120, and finally 120 × 1 = 120.
  • Step 7: Conclude that there are 120 different ways to arrange the 5 books on the shelf.
  • Factorial – The number of ways to arrange 'n' distinct objects is given by 'n!', which is the product of all positive integers up to 'n'.
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