Combinations for 6-card pattern from 4-deck cards I had programmatically determined all the desired combinations of the 6-card patterns from a 4-deck cards, and now I want to apply combinatorics method to verify my computer generated results.
From my computer simulation I've determined the following patterns and combinations (it should be emphasized that I'm NOT interest in flush and straight patterns, so it is not necessary to remove any  existing flush and/or straight formations from the 6-card patterns):
6-Card Patterns and --> computer generated combinations


*

*(a) Six different ranks (example: K, J, Q, 1, 2, 3) --> 28,789,702,656 

*(b) Six of a kind (ex: 1, 1, 1, 1, 1, 1)  --> 104,104

*(c) Five of a kind (ex: 1, 1, 1, 1, 1, 4) --> 10,902,528

*(d) Four of a kind (ex: 1, 1, 1, 1, 3, 4) --> 399,759,360

*(e) Four of a kind & a pair (ex: 1, 1, 1, 1, 4, 4) --> 34,070,400

*(f) Three of a kind (ex: 1, 1, 1, 2, 3, 4) --> 6,560,153,600

*(g) Three of a kind & a pair (ex: 1, 1, 1, 2, 2, 3) --> 1,845,043,200

*(h) Three of a kind & three of a kind (ex: 1, 1, 1, 2, 2, 2) --> 24,460,800

*(i) Three-pair (ex:  5, 5, 9, 9, 3, 3) --> 494,208,000

*(j) Two-pair (ex:  5, 5, 9, 9, 3, 6) --> 15,814,656,000

*(k) One-pair (ex: 5, 5, 1, 2, 3, 4) --> 50,606,899,200

*Total combinations COMBIN(52*4,6) --> 104,579,959,848 


Edit: 
With inputs from Lulu and John, I then realized of error in my program, and the simulation results were subsequently updated, and I was able to verify my simulation results.
Thanks to everyone for your inputs.
 A: Five of a kind: Choose which rank is the five of a kind $(13)$, and then which particular five cards of that rank you get ($_{16}C_5$). Then choose the sixth different card from what's left ($192$).
So, $13 \cdot 4368 \cdot 192 = 10902528$ combinations.
Looks like you were successful for that one, in my book.
Let's try another. How about three of a kind and a pair:
Choose which rank is the three of a kind $(13)$ and the particular three cards of that rank ($_{16}C_3$). Choose the rank of the pair $(12)$, and the two particular cards ($_{16}C_2$). Choose the sixth card from the other ranks $(176)$.
So, $13 \cdot 560 \cdot 12 \cdot 120 \cdot 176 = 1845043200$ combinations.
Well, that one doesn't look quite right.
Anyway, I'd try to calculate the answer by hand (which is fairly straightforward) then compare with your computer simulation for each one.
Side note: I'm not clear as to whether you are counting every seven of diamonds (say) as distinct, or the same. (Example, you mixed a Steelers deck, a Patriots deck, a Cowboys deck, and a Broncos deck, vs mixing four identical standard Bicycle decks.) Since I got the same answer as you with the first one, I assumed you're treating them as different, since that's what I did. But I could have done multiple counts in the second one, since my answer is a lot bigger than yours.
