# Thread: Dice game problem

1. ## Dice game problem

The problem that I raise is the following one: there exists a game in which the player rolls a certain number of six faces dice and obtains a success for every six or every two fives that he obtains in the roll, for example if it was rolling five dice and rolls 5,6,5,5,5 he obtains three successes.

Then I would like to make a table that indicates the possibilities of obtaining one or more successes and exactly one, two, three and so on up to ten with a reservation of between one and ten dice.

Can anybody help me?

2. Originally Posted by Pueblic
The problem that I raise is the following one: there exists a game in which the player rolls a certain number of six faces dice and obtains a success for every six or every two fives that he obtains in the roll, for example if it was rolling five dice and rolls 5,6,5,5,5 he obtains three successes.

Then I would like to make a table that indicates the possibilities of obtaining one or more successes and exactly one, two, three and so on up to ten with a reservation of between one and ten dice.

Can anybody help me?
For the one or more successes question:

Let number of dice be n.

Consider the number of ways to roll such that no 5 and no 6 is rolled. It is 4^n.

Consider number of ways to roll such that no 6 is rolled and exactly one 5 is rolled. It is 4^(n-1) * n.

Total number of ways to roll is 6^n.

So...