Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1.$  Find the maximum value of $x^3 y^2 z.$
Question:
Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1.$  Find the maximum value of $x^3 y^2 z.$
Answer:
Let's think step by step.

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\frac{1}{432}
Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1.$  Find the maximum value of $x^3 y^2 z.$
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