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**Plato** For part b) we can choose 2, 3, 4, 5 or 6 from department A

There are seventeen employees in all, eight in department A and then nine not in department A.

If we choose only two from department A, $\displaystyle \left(^{8}\mathcal{C}_2\right)$, then we must choose four not in department A, $\displaystyle \left(^{9}\mathcal{C}_4\right)$.

You do that for each of $\displaystyle k=3,4,5,6$, $\displaystyle \left(^{8}\mathcal{C}_k\right)\left(^{9}\mathcal{C }_{6-k}\right)$

Now you add them up.

Part c) is difficult. There are nine combinations you have to calculate.

$\displaystyle \begin{array}{ccccc}

A &\vline & B &\vline & C \\

\hline

4 &\vline & 1 &\vline & 1 \\

3 &\vline & 2 &\vline & 1 \\

3 &\vline & 1 &\vline & 2 \\

2 &\vline & 2 &\vline & 2 \\

2 &\vline & 3 &\vline & 1 \\

2 &\vline & 1 &\vline & 3 \\

1 &\vline & 2 &\vline & 3 \\

1 &\vline & 3 &\vline & 2 \\

1 &\vline & 4 &\vline & 1 \\

\end{array} $