Probably of numbers in a bag

[Guest]

I have 3 bags, all which contains the numbers 1-5 inclusive.
What is the probability that, after choosing 2 numbers from each bag, the sum of all numbers is more than 26? The first number is NOT returned to it's respective bag before the 2nd number is drawn.


I can work out the total number of combinations by doing 3 * nCr(5,2) which equals 30 possible combinations, but I want to know how many of those combinations sums is above 26.
Thanks in advance.

[Guest]

**CORRECTION: total combinations is actually [tex]{5 \choose 2}[/tex] * [tex]{5 \choose 2}[/tex] * [tex]{5 \choose 2}[/tex] = 1000
Also worth nothing the size of numbers im dealing with goes into the 100s, so just working out all possible combinations is not feasible.