Chapter 1.5, Problem 7IP

To determine

How many ways can a person playing the game roll a sum less than 8.

Answer to Problem 7IP

  $20\text{ways}$

Explanation of Solution

Given :

Two cubes are numbered 1 through 6. During a game, both are rolled and the faces landing up are added.

In order to find how many ways can a person playing the game roll a sum less than 8, first making a table of dies 1, dies 2 and total, as shown below:

Dies 1	Dies 2	Total
1	1	2
1	2	3
1	3	4
1	4	5
1	6	7
2	1	3
2	2	4
2	3	5
2	4	6
2	5	7
3	1	4
3	2	5
3	3	6
3	4	7
4	1	5
4	2	6
4	3	7
5	1	6
5	2	7
6	1	7

So, there are 20 ways to roll a sum less than 8.