Question 1062142
Same answer, different way of counting.
 
There are {{{6}}} possible outcomes for each of the number cubes,
so that makes {{{6^3=216}}} possible and equally probable outcomes.
If we can tell the number cubes apart
(for example because they are different colors, or because we roll them separately), we can tell apart those 216 outcomes.
We would count 10, 10, and 8 in the red, white, and blue cubes respectively as one outcome,
10, 8, and 10 in the red, white, and blue cubes respectively as another one of the 216 equally probable outcomes,
and 8, 10, and 10 in the red, white, and blue cubes respectively as yet another one.
Of course, if the 3 cubes are identical, and they are rolled together, we could not distinguish those 3 outcomes, and we would just see that getting one 8 and two 10's is 3 times more likely than getting three 10's.

There is only way for the numbers on all 3 cubes to be 10,
but there would be {{{3}}} ways to get two 10's and one 8,
each way having the 8 appear on a different cube.
For a set of 3 different numbers, such as 10, 8 and 6,
there are {{{3!=1*2*3=6}}} permutations that would give us that set of numbers.
 
That said, what sums of numbers would be greater than 20?
We have
{{{10+10+10=30}}} , {{{8+8+8=24}}} ,
which can happen only one way each,
accounting for {{{2}}} of the {{{216}}} possible outcomes.
There are also {{{7}}} sums greater than 20, that can happen {{{3}}} different ways:
{{{10+10+8=28}}} ,
{{{10+10+6=26}}} ,
{{{10+10+4=24}}} , 
{{{10+10+2=22}}} ,
{{{10+8+8=26}}} ,
{{{10+6+6=22}}} , and
{{{8+8+6=22}}} .
Those account for {{{7*3=red(21)}}} of the  {{{216}}} outcomes.
Finally, there are {{{2}}} sums greater than 20, that can happen {{{6}}} different ways:
{{{10+8+6=24}}} , and {{{10+8+4=22}}} .
Those sums account for {{{2*6=green(12)}}} of the {{{216}}} possible outcomes.
All the other possible sums are equal or less than 20/.
The number of possible outcomes with a sum greater than 20 are
{{{2+red(21)+green(12)=35}}} of the {{{216}}} equally probable outcomes.
so, the probability that the sum of the numbers rolled is greater than 20 is
{{{highlight(35/216)}}} .
 numbers