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How many ways can 5 books be arranged on a shelf?
How many ways can 5 books be arranged on a shelf?
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Practice Questions
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Q1
How many ways can 5 books be arranged on a shelf?
60
120
100
24
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The number of arrangements of 5 distinct books is 5! = 120.
Questions & Step-by-step Solutions
1 item
Q
Q: How many ways can 5 books be arranged on a shelf?
Solution:
The number of arrangements of 5 distinct books is 5! = 120.
Steps: 7
Show Steps
Step 1: Understand that we have 5 distinct books to arrange.
Step 2: Realize that the arrangement of these books is a permutation problem.
Step 3: Recall the formula for permutations of n distinct items, which is n! (n factorial).
Step 4: For our case, n is 5 because we have 5 books.
Step 5: Calculate 5! (5 factorial), which means 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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