Question

If \( {}^{n}C_{12} = {}^{n}C_{8} \), then \( n \) is:

• A. 20
• B. 12
• C. 4
• D. 30

Hint:

Pascal's triangle is symmetric, which is the visual basis for the identity ${}^{n}C_{r} = {}^{n}C_{n-r}$.

Answer 1

The Correct Option is A

Step 1: Concept
If ${}^{n}C_{x} = {}^{n}C_{y}$, then either $x = y$ or $x + y = n$.
Step 2: Analysis
Here $12 \neq 8$, so we must have $12 + 8 = n$.
Step 3: Conclusion
$n = 20$.
Final Answer: (A)