How to calculate Colorado Lottery MatchPlay game probabilities

The colorado lottery has just introduced a new game. It is $2 for 3 lines of 6 numbers out of 38 possible. The first line can be either chosen by the player or a Quick Pick. The other 2 lines are always Quick Pick. For the Drawing, 6 numbers are pulled from the 38 possible and you win if you match 3, 4, 5, or all 6 numbers on any of your 3 lines. ALSO, if you match 5, 6, 7, 8, 9, or 10+ numbers from a combination of all 3 of your lines, you also win. 4 total ways to win.
My Question is this: How do you calculate the probabilities for this game? I can calculate "simple" lottery probabilities and even powerball, but I am not sure how to go about this one.

The Payouts are as follows
Cost to Play $2
Line Play: (3 lines)
Match 6 win $100,000+ (progressive jackpot)
Match 5 win $500
Match 4 win $10
Match 3 win $2

Combined Play (Match any of your 18 possible numbers to the 6 winning numbers)
Match 10+ win $1000
9: $250
8: $50
7: $10
6: $5
5: $2

Colorado Lottery Matchplay web site
Thanks

The first group of payouts are calculated the same way as a simple lottery.
match - combos
6 - 1
5 - 192
4 - 7,440
3 - 99,200
2 - 539,400
1 - 1,208,256
0 - 906,192
total - 2,760,681

You should be able to calculate the return yourself.
You have 3 lines, so multiply the return by 3. 0.16981317290915 * 3 = 0.50943951872744
I'll go over the calulattions for geting 5 on the combined play.
You can have 5 matches on the 1st line, and 0 on the 2nd and 3rd (500). 192 * 906,192 * 906,192= 157667316645888
You can also have 0 on the 1st , 5 on the 2nd , 0 on the 3rd(050). and 005 = 157667316645888 *3 = 473001949937664
Other ways to have 5 are 410, 320 (6 differant permutations each) and 311, 221 (3 perms. each)
Add up all these numbers and divide by 2,760,681^3. You should get 0.086947103855684
Lather, rinse, repeat.
Here is the final probablities:
10+ - 0.0000195648158
9 - 0.000184567985942
8 - 0.001367901195056
7 - 0.007451198157757
6 - 0.029813119905034
5 - 0.086947103855684
4-0 - 0.87421654408473

Hope that makes sence if not just ask any questions.

Wow, so you have to use brute force to figure that one out, huh? No simple excel sheet formulas, but rather manually calculating the odds of each combination of getting 5, then 6...then 10, and adding them all together? No wonder I couldn't figure that one out.
Thanks!