CPM Homework Help : A2C Problem 10-124

A pizza parlor has $12$ toppings other than cheese. How many different pizzas can they create with five or fewer toppings? List all subproblems and calculate the solution.

Hint:

Answer:

$\begin{array}{l} \qquad \; \; \; \text{five toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}}\\ \qquad \; \; \text{four toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}}\\ \qquad \text{three toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}}\\ \qquad \; \; \text{two toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}}\\ \qquad \; \; \text{one toppings:}\quad \; \; \; {\color{blue}{\mathbf{?}}}\\ \underline{+\qquad \; \text{no toppings:}\quad \; \; \; {\color{blue}{\mathbf{?}}}\qquad\qquad \qquad \quad \; }\\ \; \end{array}$

$\begin{array}{l} \qquad \; \; \; \text{five toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}} {\color{red}{\boldsymbol{=792}}}\\ \qquad \; \; \text{four toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}} {\color{red}{\boldsymbol{=495}}}\\ \qquad \text{three toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}} {\color{red}{\boldsymbol{=220}}}\\ \qquad \; \; \text{two toppings:}\quad {\color{blue}{\mathbf{_{12}C_5}}} {\color{red}{\boldsymbol{=?}}}\\ \qquad \; \; \text{one toppings:}\quad \; \; \; {\color{blue}{\mathbf{?}}} \quad {\color{red}{\boldsymbol{=?}}}\\ \underline{+\qquad \; \text{no toppings:}\quad \; \; \; {\color{blue}{\mathbf{?}}} \quad {\color{red}{\boldsymbol{=?}}}\qquad \qquad \qquad }\\ \qquad \qquad \qquad \qquad \qquad \quad \; \; \; {\color{red}{\boldsymbol{=1586}\textbf{ pizzas}}} \end{array}$