There are 36 outcomes. List them out. 1,1; 1,2; 1,3; 1,4; 1,5; 1,6; .................... and so on.
If there were 3 dice, then there would be 6^3 outcomes. If there were 10 dice, there would be 6^10 outcomes. See the pattern?.
There is a quick way to find how many outcomes sum to more than 5.
That means they would have to sum to 6,7,8,9,10,11,12.
It is called a generating function.
^{2})
If we expand this we get
Look at the exponents and their corresponding coefficients(numbers in front of the x's).
Look at the exponents larger than 5 and add up their coefficients. Each number it fron of the x is how many times that sum occurs. For instance, how many ways sum to 7?. The coefficient corresponding to x^7 is 6. There are 6 ways the two dice sum to 7. So, the probability we get a sum of 7 is 6/36=1/6.
See?. Do this with your case and divide by 36 to fnd the probability. Or, you can list them out and count them up. But I do not like brute force. Especially with counting problems. It defeats the purpose.
Well done!
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