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

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

Options:

Correct Answer: 6

Solution:

The number of arrangements is 3! = 6.

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

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.

Permutations – The question tests the understanding of permutations, specifically how to arrange a set of distinct items.