Which statement best describes a permutation relative to a combination?

Which statement best describes a permutation relative to a combination?

• A. Order does not matter.
• B. Order matters in all cases.
• C. Permutations equal each other regardless of order.
• D. Permutations involve arranging objects so that order matters.

Answer: (D)

Order is what sets a permutation apart from a combination. In a permutation, the order of the chosen items matters, so different orders count as different outcomes. For example, with items A, B, and C, arranging two in a line gives AB and BA as distinct arrangements. A combination would treat those as the same selection because it ignores order. So the statement that permutations involve arranging objects so that order matters accurately describes how they are counted. The other ideas conflict with this: order not mattering describes combinations, saying order matters in all cases is too broad, and claiming all permutations are the same regardless of order ignores that AB and BA are different.

Order is what sets a permutation apart from a combination. In a permutation, the order of the chosen items matters, so different orders count as different outcomes. For example, with items A, B, and C, arranging two in a line gives AB and BA as distinct arrangements. A combination would treat those as the same selection because it ignores order. So the statement that permutations involve arranging objects so that order matters accurately describes how they are counted. The other ideas conflict with this: order not mattering describes combinations, saying order matters in all cases is too broad, and claiming all permutations are the same regardless of order ignores that AB and BA are different.