How many different combinations would you get from rolling 5 6-sided dices?

Question

Please xplain how you got your anwser. :D

Umm, it would be 7776? Right?

Answer 1

It would not be 7776 (6*6*6*6*6) because that number comes from the formula for permutations with repetition (i.e., the same number can be used more than once). 7776 includes 12345, 52431, 54321, etc. which are not valid combinations.

The formula you want is for combinations with repetition:
(n+r-1)! / (r! * (n-1)!)
(6+5-1)! / (5! * (6-1)!)
10! / (5!*5!)
(10*9*8*7*6) / 5!
30240/120
252 is your answer.

Answer 2

Edit: I answered this for 6 dice, Now I have to change it for 5
Ok 3 answers
If the total is all that matters then its 6-30 which is 15 different totals
If the order doesn't matters then it's 252 different combinations
Filnally if the order matters it's 6^5 which is 7776 different combinations

needing more explanation is the scenario where order doesn't matter. This is where 11116, 11161, 11611, 16111, 61111 are all the same.

I don't know how to explain this but I used a chart
6 5 4 3 2 1
21 15 10 6 3 1
56 35 20 10 4 1
126 70 35 15 5 1
252 126 56 21 6 1
462 210 84 28 7 1

The best way to explain how i created this chart is this
2 dice
6---5---4---3--2---1 = 21
11 22 33 44 55 66
12 23 34 45 56
13 24 35 46
14 25 36
15 26
16

Then to get
21 15 10 6 3 1
So with 3 dices, 21 is all the combinations that start with 1, 15 is all the combinations that start with 2, 10 is all the combinations that start with 3, and so on

Then I recognized the pattern. I know this explanation isn't all that great, but try it out, and maybe you'll see the pattern.

Answer 3

The number of results is as follows:
1 die = 6 Totals of (1-6)
2 dice = 36 Totals of (2-12)
3 dice = 216 Totals of (3-18)
4 dice = 1926 Totals of (4-24)
5 dice = Totals 7776 (5-30)

However, I'm not sure if you are asking total results, as in
1,1, 2, 4, 5 as opposed to
1, 5, 2, 4 1 Which are different combinations, but similar.

for example
2 six sided dice yield 36 combinations, where
1,1 occurs once
1,2 occurs twice
etc....
6,6 occurs once

Sorry, I can't help you more. Probability is not my thing.

Answer 4

It depends entirely on whether you can distinguish the dice from each other.

That is, is 1-1-1-1-6 different from 1-1-1-6-1?

If so, then the answer is 6^5 = 7776.

If not, it's more complicated. :-)
.

Answer 5

In combinations, order doesn't matter. So, rolling 1-2-3 is the same as rolling 3-2-1.

If you roll five 6-sided dice, the smallest total you could get is 5. The largest total you could get is 30. You could also get anything in-between.

So, the total number of combinations (unique outcomes) is 26.

If order does matter, it's not a combination, but rather a permutation. In this case, the number of outcomes would be 6^5, or 7776.

Answer 6

yea 7776
6*6*6*6*6