Okay, so myself and another person were playing around with some programming of a 2 handed pinochle deck. The other person simulated 34K deals or so and came up with 1 variation of a hand 2 times... then they simulated another 250K deals and came up with 0 more instances. How do I calculate the probability of such a variation of that hand?

Pinochle deck:
4x of each ace, 10, king, queen & jack.

Hand in question... triple Aces/Kings/Queens/Jacks (i.e. 3 of each in each suit, so 12 cards).

I was thinking it would start like:
12/80 * 11/79 * 10/78 * 9/77 * 8/76 * 7/75 * 6/74 * 5/73 * 4/72 * 3/71 * 2/70 * 1/69

but then I thought that may be the probability of getting any of the given 4 with all 12 cards dealt in order.

so maybe the below would work on getting any ace/king/queen/jack as the first card, then the remainin 11, but that's still over the next 11 cards.

48/80 * 11/79 * 10/78 * 9/77 * 8/76 * 7/75 * 6/74 * 5/73 * 4/72 * 3/71 * 2/70 * 1/69

Since a pinochle hand contains 20 cards, how do I calculate the probability of getting 12/16 specific cards in that 20 card hand? My above numbers may be off still.

First may be 64/80 instead of 48 because there are 4 of each card of each suit so 4*4*4...

Can anyone help?