NDA2026MathematicsPermutation and CombinationActual
If n= ^ m C₂ then what is ^ n C₂ equal to ?
Options
- A^ m+1 C₄
- B2 ^ m+1 C₄
- C3 ^ m+1 C₄
- D^ m+2 C₄
Correct answer
C. 3 ^ m+1 C₄
Step-by-step solution
Given n = ^ m C₂ = m(m-1) 2 Evaluating ^ n C₂ = n(n-1) 2 Substituting the value of n : ^ n C₂ = m(m-1) 2 ( m(m-1) 2 - 1 ) 2 ^ n C₂ = m(m-1)(m^2 - m - 2) 8 Factorizing m^2 - m - 2 = (m-2)(m+1) : ^ n C₂ = (m+1)m(m-1)(m-2) 8 Multiplying and dividing by 3 : ^ n C₂ = 3 (m+1)m(m-1)(m-2) 24 ^ n C₂ = 3 ^ m+1 C₄ Answer: 3 ^ m+1 C₄