AMC 8 2022 (Problem 8)

What is the value of

\dfrac{1}{3}\cdot\dfrac{2}{4}\cdot\dfrac{3}{5}\cdots\dfrac{18}{20}\cdot\dfrac{19}{21}\cdot\dfrac{20}{22}

\text{(A)}\;\frac{1}{462}

\text{(B)}\;\frac{1}{231}

\text{(C)}\;\frac{1}{132}

\text{(D)}\;\frac{2}{213}

\text{(E)}\;\frac{1}{22}