Outcomes With Combinations/Permutations

Question

So let's say theoretically I'm creating a dice game, where you roll 2 die, add the 2 die together and theres your number. Obviously, because we have added them, numbers such as 6 will have more outcomes than numbers 12 or 1.

How would I go about working out how many outcomes the number 6 would have using combinations/permutations

Answer 1

I am not sure what you mean by using permutations and combinations.

BTW dice is the plural noun; die is the singular noun. i.e. you roll 2 dice.

The way to answer this problem is to make a table with 1 to 6 down the left side and 1 to six across the top.

At the intersection of each row and column put the sum of number at the top + the number from the left.

There are 36 outcomes. Now just go count whatever outcomes you want. For example, you want to know how often the sum will be six. Just go into your table and count how many sixes there are!

Also it is not too difficult to derive the distribution function of the sum of 2 random variables, which is really not relevant here.