Solutions - 5070-03

(1) Set up the counting argument:

Since order does not matter, the sample space has $\left(\genfrac{}{}{0px}{}{7}{2}\right)$ outcomes. For different colors, choose one of each.

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(2) Evaluate:

$$\begin{array}{c}P[\text{different colors}]=\frac{\left(\genfrac{}{}{0px}{}{3}{1}\right)\cdot \left(\genfrac{}{}{0px}{}{4}{1}\right)}{\left(\genfrac{}{}{0px}{}{7}{2}\right)}\\ \\ \gg \gg \frac{12}{21}\gg \gg \frac{4}{7}\end{array}$$