Chapter 9, Problem 92RE

To determine

To Find:The total number of combinations of sandwich possible.

Answer to Problem 92RE

  $4200$

Explanation of Solution

Given:A local sandwich shop offers five different breads, four different meats, three different cheeses, and six different vegetables. A customer can choose one bread, one or no meat, one or no cheese, and up to three vegetables.

We have to choose one bread from five different breads

i.e.

  $C{}_1$

One or no meat from four different types

  $C{}_0+C{}_1$

One or no cheese from three different cheese

  $C{}_0+C{}_1$

Up to three vegetables from six different vegetables

  $C{}_0+C{}_1+C{}_2+C{}_3$

Then

The number of possible combination becomes

  $\begin{array}{l}C{}_1(C{}_0+C{}_1)(C{}_0+C{}_1)(C{}_0+C{}_1+C{}_2+C{}_3)\\ =5(1+4)(1+3)(1+6+15+20)\\ =5\times 5\times 4\times 42\\ =4200\end{array}$