The math will be the same as before. I'm assuming you're interested in knowing what the odds of getting 4 aces, split, and getting 4 blackjacks? If so, your 3 face cards and 1 ten make it missleading.
If you do indeed mean misleading, then simply update RS's equation above so instead of searching for "any 10 valued card" it's literally any "10" left in the deck.Simple Explanation of Simple Statistics
When you ask what are the odds of "this and this and this and this..." etc... the key word here is "and" which means the probability will be multiplicative. P(A)*P(B)*...etc.
When you ask what are the odds of "this or that or that or that..." etc... the key word here is "or" which means the probability will be additive. P(A) + P(B) +... etc.Your Example
Thus, take them in order that they have to happen...
P(first 2 cards ace) = P(first card ace AND second card ace) = P(1st Ace) * P(2nd Ace) = (24/312) * (23/311)
P(next card 3rd ace) = (22/310)
P(next card 4th ace) = (21/309)
P(next card 1st face) = (96/308)
P(next card 2nd face) = (95/307)
P(next card 3rd face) = (94/306)
P(next card 4th face) = (93/305)
Remember: you said "AND THIS AND THIS AND THIS" so they're all multiplied together. That's where the
(24*23*22*21*96*95*94*93) / (312*311*310*309*308*307*306*305)
comes from... If you wanted to know 3 face values and the last one an actual "10" then you would change the 96, 95, 94, and 93 values to their respective values (how many KQJ's in 6 decks, then how many "10's" in 6 decks).
So if you actually multiply and divide those numbers out... you get: 20,332,308,648,960 / 82,024,863,079,573,814,400 = .00000025. If you just wanted to use ONLY the simple calculator on your computer you could do this, then just guess and check 1/x and see what comes up with 6 zeros and 25... hint: since they already solved it start with something like 4,000,000 ;-)... thus, a 1 in ~4,000,000 chance.
Playing it correctly means you've already won.