How many different ways can 3 men and 2 women be seated in a row?

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Question: How many different ways can 3 men and 2 women be seated in a row?

Options:

Correct Answer: 120

Solution:

The number of arrangements of 5 people (3 men + 2 women) is 5! = 120.

How many different ways can 3 men and 2 women be seated in a row?

How many different ways can 3 men and 2 women be seated in a row?

Step 1: Identify the total number of people to be seated. In this case, there are 3 men and 2 women, which makes a total of 5 people.
Step 2: Understand that seating arrangements can be calculated using the factorial of the total number of people. The factorial of a number (n!) is the product of all positive integers up to that number.
Step 3: Calculate the factorial of 5 (which is the total number of people). This is written as 5!.
Step 4: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 5: Conclude that there are 120 different ways to arrange 3 men and 2 women in a row.

Permutations – The question tests the understanding of permutations, specifically how to arrange a set number of distinct objects (in this case, people) in a specific order.