Mastery Check Solutions

1. How many different dinner arrangements can be served?

$\begin{array}{ccc}\underline{ 5 }& \underline{ 6 }& \underline{ 2 }\\ h& e& d\end{array}=60$

There are 60 dinner arrangements that can be served.

2. The staff reports to Chef Julianne that dinner guests want 3 more dessert options and a soup or salad with dinner. How many more options would dinner guests have?

$$\begin{gathered} \begin{array}{cccc}\underline{ 5 }& \underline{ 6 }& \underline{ 2+3 }& \underline{ 2 }\\ h& e& d& s\end{array}=300 \\ 300–60=240 \end{gathered}$$

Adding 3 more desserts and the choice of a soup or salad gives diners 240 more possible dinners to select from.

3. Eight staff members are available to do the restaurant’s prep work before opening, but Chef Julianne determines that only six people are needed. If each person is assigned a specific job when they arrive, how many possible ways can Chef Julianne assign her staff?

$\begin{array}{rcl}nPr \left(8, 6\right)& =& \frac{8!}{\left(8–6\right)!}\\ & =& \frac{8!}{2!}=\frac{8·7·6·5·4·3·\cancel{2!}}{\cancel{2!}}\\ nPr \left(8, 6\right)& =& 20,160\end{array}$

Chef Julianne can arrange her staff 20,160 different ways.