Question

Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`

Answer 1

`""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
If ⁿC_x = ⁿC_y, then either x = y or x = n − y
∴ r −1 = r + 1 or r − 1 = 2n − (r + 1)
But r − 1 = r + 1 is not possible
∴ r − 1 = 2n − (r + 1)
∴ r + r = 2n
∴ n = r