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

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

Options:

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

Correct Answer: 120

Solution: 

The number of ways to select and arrange 5 books is 5! = 120.

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

Practice Questions

Q1
How many ways can 5 different books be selected and arranged on a shelf?
  1. 120
  2. 60
  3. 30
  4. 24

Questions & Step-by-Step Solutions

How many ways can 5 different books be selected and arranged on a shelf?
Correct Answer: 120
  • Step 1: Understand that we have 5 different books.
  • Step 2: Realize that we want to arrange all 5 books on a shelf.
  • Step 3: Know that arranging items is a permutation problem.
  • Step 4: The formula for arranging 'n' different items is 'n!'.
  • Step 5: Since we have 5 books, we use the formula 5!.
  • Step 6: Calculate 5! which means 5 x 4 x 3 x 2 x 1.
  • Step 7: Perform the multiplication: 5 x 4 = 20, then 20 x 3 = 60, then 60 x 2 = 120, and finally 120 x 1 = 120.
  • Step 8: Conclude that there are 120 different ways to select and arrange the 5 books.
  • Permutations – The question tests the understanding of permutations, specifically how to arrange a set of distinct items.
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