Find the probability that a specific player gets 4 kings and another specific player gets exactly 2 Aces in a hand at whist, given that there are 4 players and 52 playing cards.
Here's what i did:
The first specific player gets 4 kings out of 4kings from the deck by 4C4 and the rest 9 cards out of the remaining 44 (=52-4kings-4aces) by 44C9. So probability becomes
p1 = (4C4)*(44C9)/(52C13)
now to the other player, i gave 2 aces from the 4 available by 4C2 and the remaining 11 cards by 37C11. So, probability becomes
p2 = (4C2)*(37C11)/(39C13)
Hence, final probability becomes
p1*p2 = 7.050960*10^(-4)
which is incorrect. Where did i go wrong?