Linking permutations and combinations: If P(n, r) = 720 · C(n, r), find r.

Introduction / Context:Permutation and combination are related by P(n, r) = C(n, r) * r!. The equation given directly identifies r! as a numeric constant times C(n, r), enabling a quick solution for r.

Given Data / Assumptions:P(n, r) = 720 · C(n, r).

Concept / Approach:Use the identity P(n, r) = C(n, r) · r!. If C(n, r) ≠ 0, divide both sides by C(n, r) to isolate r!.

Step-by-Step Solution:

Verification / Alternative check:Plug r = 6: indeed P(n, 6) = C(n, 6) · 6! = 720 · C(n, 6).

Why Other Options Are Wrong:5! = 120, 4! = 24, 7! = 5040; none equal 720.

Common Pitfalls:Trying to solve for n unnecessarily; r is determined solely by 720.

Final Answer:6