Solving from ratios of consecutive combinations: If C(n, r−1) = 36, C(n, r) = 84, C(n, r+1) = 126 (repeated for clarity), confirm n and r and provide reasoning.

Introduction / Context:
This reiterates and confirms the ratio-based method for adjacent binomial coefficients to ensure conceptual clarity for learners reviewing contiguous values in Pascal rows.

Given Data / Assumptions:
Same as earlier: 36, 84, 126 for C(n, r−1), C(n, r), C(n, r+1) respectively.

Concept / Approach:
Use identities of consecutive ratios to produce two linear equations in n and r, then solve.

Step-by-Step Solution:

Verification / Alternative check:
Direct substitution matches all three numbers.

Why Other Options Are Wrong:
Other pairs fail one or more of the three equalities.

Common Pitfalls:
Mixing the ratio direction or losing the +1 term.

Final Answer:
n = 9, r = 3