Chapter 11, Problem 7PSQ

To determine

To find the different combinations of the lunch special possible.

Answer to Problem 7PSQ

The different combinations of the lunch special possible are,

  ${}_5{C}_1{+}_4{C}_1{+}_{3}C=60$

Explanation of Solution

Given information:the expression for possible combination from given dataset,

  ${}_5{C}_1{\times }_4{C}_1{\times }_3{C}_1$

Calculation: the given combination can be evaluated as,

  $\begin{array}{l}{}_5{C}_1{\times }_4{C}_1{\times }_3{C}_1\\ {}_5{C}_1{+}_4{C}_1{+}_3{C}_1\text{=}\frac{{}_5{P}_1}{1!}\times \frac{{}_4{P}_1}{1!}\times \frac{{}_3{P}_1}{1!}\left[\text{use formula of combination }\right]\\ {}_5{C}_1{+}_4{C}_1{+}_{3}C=\frac{5}{1}\times \frac{4}{1}\times \frac{3}{1}\left[\text{write as products}\right]\\ {}_5{C}_1{+}_4{C}_1{+}_{3}C=5\times 4\times 3\left[\text{multiply}\right]\\ {}_5{C}_1{+}_4{C}_1{+}_{3}C=60\end{array}$

Therefore,

The different combinations of the lunch special possible are,

  ${}_5{C}_1{+}_4{C}_1{+}_{3}C=60$