Question

Find n if ²ⁿC_r–1 = ²ⁿC_r+1 

Answer 1

²ⁿC_r–1 = ²ⁿC_r+1 

We know that if ⁿC_r = ⁿC_y, then x = y or x + y = n

∴ r – 1 + r + 1 = 2n   ...[∵ x = y is not possible]

∴ 2r = 2n

∴ r = n

∴ n = r.