# Simple statistics Combination/Permutation problem

• May 24th 2012, 10:12 AM
matzematze
Simple statistics Combination/Permutation problem
Hello, I've recently joined this forum to get help in mathematics. I am going to be studying in an engineering field next year as an undergrad. Over the summer, I've taken up computer programming as a hobby and I'm having a hard time with some statistical programs I'm trying to make. Here is my simple problem:

How many different combinations of two numbers can add up to make 8? Each number can be no greater than 6.

This is exactly the probability of rolling an 8 when rolling two dice. I know that the answer to this question is 5, as in there are 5 different combinations of 2 numbers that will add up to equal 8. For example:

1. 2 + 6
2. 6 + 2
3. 3 + 5
4. 5 + 3
5. 4 + 4

Therefore, there is a 5/36 chance of rolling an 8 when rolling 2 dice with 6 faces each.

I want to extract some basic principle or formula out of this so that I can do the same thing with more dice and more or less faces on each die.

Thank you very much, I appreciate any responses.

(I'm not here just to leech on others. I plan contributing to the help threads where I'm qualified to actually help like calculus. )
• May 24th 2012, 11:02 AM
Plato
Re: Simple statistics Combination/Permutation problem
Quote:

Originally Posted by matzematze
How many different combinations of two numbers can add up to make 8? Each number can be no greater than 6.
This is exactly the probability of rolling an 8 when rolling two dice. I know that the answer to this question is 5, as in there are 5 different combinations of 2 numbers that will add up to equal 8. For example:
1. 2 + 6
2. 6 + 2
3. 3 + 5
4. 5 + 3
5. 4 + 4
Therefore, there is a 5/36 chance of rolling an 8 when rolling 2 dice with 6 faces each.

If you go to this webpage
Scroll down to the expanded form you will see one term $5x^8$.
The coefficients tell us the number of ways to add the dice. $4x^5$ means we get five in four ways.

If you now change the power from $[~~]^2$ to $[~~]^4$ those new coefficients tell us the number of ways to add four dice.
• May 24th 2012, 11:17 AM
matzematze
Re: Simple statistics Combination/Permutation problem
Ah that's brilliant. I have no idea how that works but it works.

Thanks.
• May 24th 2012, 11:23 AM
matzematze
Re: Simple statistics Combination/Permutation problem
Is there a name for this procedure that I can Google in order to learn more on how it works?