What is the value of n, if the coefficients of the second term of (x – y)³ is equal to the third term of the expansion (x + y)ⁿ?

The correct answer is:

3

STEP BY STEP SOLUTION
Coefficient of the second term of (x – y)³ is ³C₁, and the coefficient of the third term of the expansion (x + y)ⁿ is ⁿC₂.
³C₁ = ⁿC₂
3 = n!÷2!(n–2)!
6 = n(n−1)(n−2)!÷(n–2)!
6 = n² – n
n² – n – 6 = 0
n² – 3n + 2n – 6 = 0
(n – 3) (n + 2) = 0
n = 3, – 2

Since n cannot be negative, n = 3.