Which option correctly describes a permutation?

Which option correctly describes a permutation?

• A. Permutations are selections where order does not matter.
• B. Permutations are a type of combination.
• C. Permutations are the arranged sequences where the order matters.
• D. Permutations are calculated by adding the first two factorials.

Answer: (C)

Permutations count the number of ways to arrange r items from a set of n when the order matters. The key idea is that AB and BA are different ordered outcomes, so the sequence in which you place items matters. If order didn’t matter, you’d be counting combinations, where AB and BA are considered the same. That distinction is why the description focused on arranged sequences where the order matters is correct. The notion that permutations are a type of combination is inaccurate because combinations ignore order. And the idea of simply adding factorials doesn’t describe how permutations are counted; the standard method uses factorials in a ratio n!/(n−r)!, capturing all the distinct orders of the chosen items. So the described statement matches the essential feature of a permutation: an ordered arrangement.

Permutations count the number of ways to arrange r items from a set of n when the order matters. The key idea is that AB and BA are different ordered outcomes, so the sequence in which you place items matters. If order didn’t matter, you’d be counting combinations, where AB and BA are considered the same. That distinction is why the description focused on arranged sequences where the order matters is correct. The notion that permutations are a type of combination is inaccurate because combinations ignore order. And the idea of simply adding factorials doesn’t describe how permutations are counted; the standard method uses factorials in a ratio n!/(n−r)!, capturing all the distinct orders of the chosen items. So the described statement matches the essential feature of a permutation: an ordered arrangement.