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, coefficient of y^4 is C(n,4)=x. In (1+3y)^n, coefficient is C(n,4)·3^4 = x·81 = 81x.
Hint
Compare the binomial expansions: (1+3y)^n = Σ C(n,k) 3^k y^k.