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In how many ways can 3 different trophies be arranged on a shelf?

Practice Questions

Q1
In how many ways can 3 different trophies be arranged on a shelf?
  1. 6
  2. 12
  3. 18
  4. 24

Questions & Step-by-Step Solutions

In how many ways can 3 different trophies be arranged on a shelf?
  • Step 1: Understand that we have 3 different trophies to arrange.
  • Step 2: Recognize that arranging trophies means we are looking for different orders in which they can be placed.
  • Step 3: Use the factorial notation 'n!' to represent the number of ways to arrange 'n' items. Here, 'n' is 3 because we have 3 trophies.
  • Step 4: Calculate 3! (3 factorial), which means 3 × 2 × 1.
  • Step 5: Perform the multiplication: 3 × 2 = 6, and then 6 × 1 = 6.
  • Step 6: Conclude that there are 6 different ways to arrange the 3 trophies on the shelf.
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