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How many ways can 5 different books be arranged on a shelf?
How many ways can 5 different books be arranged on a shelf?
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Practice Questions
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Q1
How many ways can 5 different books be arranged on a shelf?
60
120
100
80
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The number of arrangements of 5 different books is 5! = 120.
Questions & Step-by-step Solutions
1 item
Q
Q: How many ways can 5 different books be arranged on a shelf?
Solution:
The number of arrangements of 5 different books is 5! = 120.
Steps: 7
Show Steps
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.
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