Chapter 12.6, Problem 28SR

a.

To determine

To explain do the outcomes of rolling the four dice represents permutations or combinations.

Answer to Problem 28SR

The rolling of four dice represent permutations.

Explanation of Solution

Given information:

Each player rolls four dice at the same time

The outcome of rolling of four dice represents permutations because in the outcome of rolling of four dice the order is important where in case of combinations the order is not important.

Use definition of permutation and combination.

b.

To determine

To write the number outcomes possible.

Answer to Problem 28SR

Number of possible outcome is 360.

Explanation of Solution

Given information:

Each player rolls four dice at the same time.

The number of possible outcomes can be calculated using permutation formula:

  $\begin{array}{l}P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\\ P\left(6,4\right)=\frac{6!}{\left(6-4\right)!}\\ P\left(6,4\right)=\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{2\cdot 1}\\ P\left(6,4\right)=360\end{array}$

Therefore,

Number of possible outcome is 360.

c.

To determine

To calculate the probability of four dice showing the same number on a single roll.

Answer to Problem 28SR

The Probability of four dice showing the same number $=\frac{1}{60}$

Explanation of Solution

Given information:

Each player rolls four dice at the same time.

The probability of all four dice showing the same number.

There are six numbers on the dice therefore six outcomes shows same number on the four dice .

  $P\left(\text{all numbers are same}\right)=\frac{6}{360}=\frac{1}{60}$

Therefore,

Probability of four dice showing the same number $=\frac{1}{60}$