Chapter 8.2, Problem 8.33E

(a)

To determine

To calculate in how many different ways are there to order a cone with two scoops if you care about the order of flavours with $28$ flavours to choose from.

Answer to Problem 8.33E

  $784$

Explanation of Solution

Since order is important, use multiple counting principle:

  $28\times 28=784$

(b)

To determine

To calculate in how many different ways are there to order a cone with two scoops of different flavors if you care about the order of flavours with $28$ flavours to choose from.

Answer to Problem 8.33E

  $756$

Explanation of Solution

Since order is important, we need to use permutation:

  $\begin{array}{l}P=\frac{28!}{(28-2)!}\\ =28\times 27\\ =756\end{array}$

(c)

To determine

To calculate in how many different ways are there to order a cup with two scoops of ice cream if you don’t care about the order of flavours with $28$ flavours to choose from.

Answer to Problem 8.33E

  $378$

Explanation of Solution

Since order is not important, we need to use combination:

  $\begin{array}{l}C=\frac{28!}{(28-2)!2!}\\ =\frac{28\times 27}{2}\\ =378\end{array}$

(d)

To determine

To calculate in how many different ways are there to order a cup with two scoops of different flavors if you don’t care about the order of flavours with $28$ flavours to choose from.

Answer to Problem 8.33E

  $392$

Explanation of Solution

Since order is not important and since every combination will appear twice:

  $\begin{array}{l}\frac{28\times 28}{2}\\ =392\end{array}$