How many ways can 3 men and 2 women be arranged in a line if the men must be tog

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Question: How many ways can 3 men and 2 women be arranged in a line if the men must be together?

Options:

Correct Answer: 120

Solution:

Treat the 3 men as one unit. So, we have 3 units (MMM, W, W). Arrangements = 4! * 3! = 24 * 6 = 144.

How many ways can 3 men and 2 women be arranged in a line if the men must be together?

How many ways can 3 men and 2 women be arranged in a line if the men must be together?

Correct Answer: 144

Step 1: Treat the 3 men as one single unit. This means we consider them as 'MMM'.
Step 2: Now, we have 3 units to arrange: 'MMM', 'W', and 'W'.
Step 3: Calculate the number of ways to arrange these 3 units. This is done using the factorial of the number of units: 3! (which is 3 x 2 x 1 = 6).
Step 4: Next, we need to arrange the 3 men within their unit 'MMM'. The number of ways to arrange 3 men is 3! (which is also 6).
Step 5: Multiply the number of arrangements of the units by the arrangements of the men: 3! (for units) * 3! (for men) = 6 * 6 = 36.
Step 6: Therefore, the total number of ways to arrange 3 men and 2 women in a line, with the men together, is 36.

Permutations – The arrangement of objects in a specific order, considering the grouping of men as a single unit.
Factorials – The mathematical operation used to calculate the number of arrangements of a set of items.
Grouping – The concept of treating multiple items as a single unit to simplify arrangement problems.