Which statement is true about permutations versus combinations?

• A. Permutations count order; combinations do not.
• B. Permutations ignore order; combinations consider order.
• C. Permutations and combinations share the same formula.
• D. Combinations are always greater than permutations for the same n and r.

Answer: (A)

The essential idea is how order affects counting. In permutations, the sequence matters: picking items in a certain order produces distinct results. For example, from three items A, B, C, choosing two gives six different ordered arrangements: AB, AC, BA, BC, CA, CB. In contrast, combinations ignore the order of the chosen items. From the same set, choosing two items yields three distinct groups: {A,B}, {A,C}, {B,C}. The same two items in a different order aren’t counted separately.

That difference shows why the statements are true or false. The fact that the count for permutations uses nP r = n!/(n−r)! while combinations use nC r = n!/(r!(n−r)!) reflects the order distinction: the r! in the denominator for combinations removes the order factor. So it’s correct to say permutations count order, while combinations do not.