Question

Find n if `""^"n""C"_8 = ""^"n""C"_12`

Answer 1

`""^"n""C"_8 = ""^"n""C"_12`

If ⁿC_x = ⁿC_y, then either x = y or x = n − y

∴ 8 = 12 or 8 = n − 12
But 8 = 12 is not possible
∴ 8 = n – 12
∴ 8 + 12 = n
∴ 20 = n
∴ n = 20