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The coefficient of x^(20) in the expansi...

The coefficient of `x^(20)` in the expansion of `(1+3x+3x^(2)+x^(3))^(20)` is
(1) `.^(60)C_(40)`
(2) `.^(30)C_(20)`
(3) `.^(15)C_(2)`
(4) `.^(60)C_(10)`

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To find the coefficient of \( x^{20} \) in the expansion of \( (1 + 3x + 3x^2 + x^3)^{20} \), we can follow these steps: ### Step 1: Simplify the Expression The expression \( 1 + 3x + 3x^2 + x^3 \) can be recognized as a binomial expansion. Specifically, it can be rewritten as: \[ (1 + x)^3 \] This is because: ...
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