Question

What is the value of \( ^nC_{n-1} \)?

• A. \(1 \)
• B. \(n! \)
• C. \(n \)
• D. \(0 \)

Hint:

Remember the symmetry property of combinations: \( ^nC_r=\, ^nC_{n-r}\). Thus \( ^nC_{n-1}=\, ^nC_1=n\).

Answer 1

The Correct Option is C

Concept: Combination formula: ⁿCᵣ = n!/(r!(n–r)!). A key symmetry property is ⁿCᵣ = ⁿCₙ₋ᵣ.

Step 1: Apply symmetry.
ⁿCₙ₋₁ = ⁿC₁. By formula: n!/(1!(n–1)!) = n.

Final Answer: n (option C).