# Thread: How many ways can you roll an even number sum if you have the choice to use up to 5 d

1. ## How many ways can you roll an even number sum if you have the choice to use up to 5 d

How many ways can you roll an even number sum if you have the choice to use up to 5 dice?

2. ## Re: How many ways can you roll an even number sum if you have the choice to use up to

even number sums will be 1/2 the total sums for a given number of dice

There are $6^k$ total possible combos of $k$ dice. Half these combos will sum to an even number.

So we have

$n = 3 + 18 + 108 + 648 + 3888 = 4665$ total ways to roll an even sum of up to 5 dice.

3. ## Re: How many ways can you roll an even number sum if you have the choice to use up to

Originally Posted by Unrated063
How many ways can you roll an even number sum if you have the choice to use up to 5 dice?
First please do not use any special fonts or colors when posting. It just gets in the way and needs to be removed.

Look at the expansion of the generating function: HERE .
The sum of the coefficients of terms with even exponents is:
$1+15+70+210+470+826+1190+1420+1190+826+270+70+15+ 1=6574$

Please note that these sums include using zero to five dice on any toss.
If you must use five dice then look HERE Sum the coefficients of terms with even exponents.
If you need only "at least one die must be used". Look HERE