Question Detail
Question
If the coefficient of \( y^4 \) in \( (1 + y)^n \) is \( x \), find the coefficient of \( y^4 \) in \( (1 + 3y)^n \).
Correct Answer
Option A is the correct answer.
Detailed Explanation
In (1+y)^n, the coefficient of y^4 is C(n,4) = x. In (1+3y)^n, the term containing y^4 is C(n,4) (3y)^4 = C(n,4) * 81 y^4. So the coefficient is 81 * C(n,4) = 81x.
Hint
Use the binomial theorem: (a+b)^n = Σ C(n,k) a^{n-k} b^k. Compare the two expansions, noting that the 3 is inside the power.