What is a permutation?

What is a permutation?

• A. A selection of items without regard to order.
• B. A function mapping items to outcomes.
• C. A comparison of two sequences.
• D. An arrangement of items where order matters, often used when counting possible outcomes.

Answer: (D)

An arrangement of items where order matters is what a permutation describes. When you count outcomes where the sequence of items is important, each different order counts as a distinct result. For example, with three items, choosing two in order yields AB, BA, AC, CA, BC, CB—six possible outcomes. This shows why order matters: rearranging the same items creates a different outcome. This idea contrasts with cases where order isn’t important, where AB and BA would be considered the same. A function mapping items to outcomes is a broader concept not inherently about counting specific ordered arrangements, and a simple comparison of sequences doesn’t capture the counting focus of permutations. So, the best understanding is that a permutation is an arrangement of items where order matters, often used when counting possible outcomes.

An arrangement of items where order matters is what a permutation describes. When you count outcomes where the sequence of items is important, each different order counts as a distinct result. For example, with three items, choosing two in order yields AB, BA, AC, CA, BC, CB—six possible outcomes. This shows why order matters: rearranging the same items creates a different outcome.

This idea contrasts with cases where order isn’t important, where AB and BA would be considered the same. A function mapping items to outcomes is a broader concept not inherently about counting specific ordered arrangements, and a simple comparison of sequences doesn’t capture the counting focus of permutations. So, the best understanding is that a permutation is an arrangement of items where order matters, often used when counting possible outcomes.