In how many ways can 5 different fruits be arranged in a row?

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Question: In how many ways can 5 different fruits be arranged in a row?

Options:

Correct Answer: 120

Solution:

The number of arrangements of 5 different fruits is 5! = 120.

In how many ways can 5 different fruits be arranged in a row?

In how many ways can 5 different fruits be arranged in a row?

Step 1: Understand that we have 5 different fruits to arrange.
Step 2: Recognize that arranging items in a row is a permutation problem.
Step 3: The formula for the number of arrangements (permutations) of 'n' different items is 'n!'.
Step 4: In this case, 'n' is 5 because we have 5 different fruits.
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 different fruits in a row.

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