Wanted to find out is this is Permutations?

I have 5 Dice (Die) and I want to print out all possible combinations / Permutations for the 5 Dice and their total.

i.e.
1 2 3 4 5 sum= 15
6 6 6 6 6 sum= 30

Anybody know how I can do this?

Many thanks,

Jim

If you include order, then this is sort of a permutation problem, but you have to choose values for the dice as well as order them, so its more than that.

>I have 5 Dice (Die)
Dice: die is singular (think of mice=plural)

>and I want to print out all possible
>combinations / Permutations for the 5 Dice and their total.

Ouch. There are 6^5 = 7776 outcomes (including order) i hope you have a lot of paper.

>Anybody know how I can do this?

You should be able to write (or get someone nice to write) a simple program to do this. However you should probably take another look at what you are trying to achieve and take a different approach.

All the best,

Rich

First, you have to decide if the order in which you pick the elements matters to you. If yes, the choices are called variations, if not, they are called combinations.

Second, you have to decide if each element can appear in a particular choice multiple times. If yes, the variations or combinations are with repetition (this is always said), if no, they are without repetition (this is often assumed).

Variations (without repetition): n!/(n-k)!
Variations with repetition: n^k

Combinations (without repetition): n!/k!(n-k)! or (n above k)
Combinations with repetition: (n+k-1)!/k!(n+k-1-k)! or (n+k-1 above k)

Variations (without repetition) for n=k (i.e., you always pick all elements, without repetition, just the order matters) are called permutations.

If you roll the same numbers on some dice and you do not care which particular dice yielded these numbers, for example you consider the following 2 patterns the same:

1 2 3 4 5 <- die
6 2 2 6 2 <- rolled numbers
2 6 6 2 2 <- rolled numbers

you have combinations with repetition:

10!/5!/5! = 9򊤋/2 = 252 ways

If you consider the above 2 patterns different, you have variations with repetition:

6⁵ = 7776 ways (about 130 pages to print!)

The number of variations with repetition is very easy to see. Assign to the die numbers 1, 2, 3, 4, 5, 6 the sextal system digits 0, 1, 2, 3, 4, 5 (i.e., subtract 1). The number of variations is the count from 0 to (55555))₆ or (100000)₆ or 6⁵.

Exp: 11111
21111
22111
22211
22221
22222
12311
12312 And etc.

I know it is monotonous, but the outcome will allow you to add the complete sum.