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{{\end{equation}{ \\ {} &= \frac{176! \cdot 6! } {173! \cdot 9! } = \frac{176 \cdot 175 \cdot 174}{9 \cdot 8 \cdot 7} \\ {} &= \frac{31, 900}{3} \approx 10, 633 \end{align} Surprise! I had no idea the...