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jmc

counting and probability intermediate

Problem

What is the coefficient of

x^{2} y^{6}

in the expansion of

(\frac{3}{5} x - \frac{y}{2})^{8}

? Express your answer as a common fraction.

Solution

By the Binomial theorem, this term is

(2 8) (\frac{3}{5} x)^{2} (- \frac{y}{2})^{6} = 28 \cdot \frac{9}{25} \cdot \frac{1}{64} x^{2} y^{6} = \frac{63}{400} x^{2} y^{6}

Final answer

\frac{63}{400}