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src/content/questions/comp2804/2019-fall-midterm/1/solution.md
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1. Determine combinations | ||
We choose 1 of the $f$ girls to be the president: $\binom{f}{1}=f$ | ||
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We choose 1 of the $f$ girls to be the president: $\binom{f}{1}=f$ | ||
We choose 3 of the remaining $f-1$ girls and m guys to be vice presidents: $\binom{f-1+m}{3}$ | ||
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We choose 3 of the remaining $f-1$ girls and m guys to be vice presidents: $\binom{f-1+m}{3}$ | ||
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2. Profit | ||
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Thus, the total number of ways to choose the president and vice presidents is $f \cdot \binom{f-1+m}{3}$ | ||
Thus, the total number of ways to choose the president and vice presidents is $f \cdot \binom{f-1+m}{3}$ |