NDA 2026 · PYQ · Combinations · medium
If n = ᵐC₂ then what is ⁿC₂ equal to?
- A.ᵐ⁺¹C₄
- B.2 × ᵐ⁺¹C₄
- C.3 × ᵐ⁺¹C₄✓ Correct
- D.ᵐ⁺²C₄
n = m(m−1)/2. Then ⁿC₂ = n(n−1)/2 = [m(m−1)/2] · [m(m−1)/2 − 1]/2 = m(m−1)[m(m−1) − 2]/8 = m(m−1)(m−2)(m+1)/8. Now ᵐ⁺¹C₄ = (m+1)m(m−1)(m−2)/24. So ⁿC₂ = 3 · ᵐ⁺¹C₄.
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