Chapter 8.2, Problem 8.34E

(a)

To determine

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

Answer to Problem 8.34E

  $21952$

Explanation of Solution

Since order is important, use multiple counting principle:

  $28\times 28\times 28=21952$

(b)

To determine

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

Answer to Problem 8.34E

  $19656$

Explanation of Solution

Since order is important, we need to use permutation:

  $\begin{array}{l}P=\frac{28!}{(28-3)!}\\ =28\times 27\times 26\\ =19656\end{array}$

(c)

To determine

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

Answer to Problem 8.34E

  $3276$

Explanation of Solution

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

  $\begin{array}{l}C=\frac{28!}{(28-3)!3!}\\ =\frac{28\times 27\times 26}{3\times 2\times 1}\\ =3276\end{array}$

(d)

To determine

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

Answer to Problem 8.34E

  $2744$

Explanation of Solution

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

  $\begin{array}{l}\frac{28\times 28\times 28}{8}\\ =2744\end{array}$