### Home > CCG > Chapter Ch10 > Lesson 10.3.5 > Problem10-179

10-179.

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.

 $\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 \ }\\ \$

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