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Chapter 4: Problem 50

A man just bought 4 suits, 8 shirts, and 12 ties. All of these suits, shirts, and ties coordinate with each other. If he is to randomly select one suit, one shirt, and one tie to wear on a certain day, how many different outcomes (selections) are possible?

Short Answer

Expert verified
The total number of different combinations/outfits possible is \(4 * 8 * 12 = 384\).

Step by step solution

01

Analyze the problem

Firstly, the number of combinations for each article of clothing is given. The amount of suits is 4, the amount of shirts is 8, and the amount of ties is 12. The task is finding the total amount of different outfits that can be created.
02

Apply the multiplication principle

The principle of multiplication states that if there are n ways to do one task and m ways to do another, then there are n*m ways to do both. In this case, there are 4 ways to choose a suit, 8 ways to choose a shirt, and 12 ways to choose a tie.
03

Multiply the number of ways to choose each piece

Multiply the ways to choose each piece of clothing together. This means 4 (for the suits) times 8 (for the shirts) times 12 (for the ties).

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