My way Works!!!! - it's just takes a while

Now I know the answer it's easier.

I was calculating the different numbers of possible hands but couldn't get the totals to add up to the total possible hands.
The problem appears when duplicate amounts of two suits are present - I've fixed that now.

continuing from 11,2,0,0

11,1,1,0 - 78 (ways of 11) X 13 (ways of 1) X 13 (ways of 1) X 3 (positions for the 0) X 4(suits) = 158184

10,3,0,0 - 286 ways for 10 X 286 ways for 3 X 3 X 4=981552
etc. etc. etc.
To save a very overlong post, the totals for the voids are:
4
2028
73008
158184
981552
6960096
6134700
63800880
52200720
19876428
287103960
689049504
35335872
689049504
2296831680
1684343232
459366336
4134297024
8421716160
5684658408
7895358900


Add this lot together to get: 32427298180

Divide by the total possible hands : 635013559600

Result: 0.051065521

(full calculation available on request)

I think I prefer the look of
4 * C(39, 13) - 6 * C(26, 13) + 4 * C(13, 13 ) ] / C(52, 13)
It's obviously quicker.

Nice question Guv.