a standard 52 card deck of cards is shuffled and then a 12-card hand is dealt from the deck. How many different outcomes are possible that have exactly 3 pairs, and all other cards of different denominations?

Question

zarkon · Answer

I get 53,137,244,160

anonymous · Answer

How did you get this?

anonymous · Answer

yes, can you please tell me how you got this. Its right though

zarkon · Answer

$${13 \choose 3}{4\choose 2}^3{10\choose 6}{4\choose 1}^6$$

anonymous · Answer

How did you get 10C6 and 4C1*6?

anonymous · Answer

10C6 is because you already chose 3 for the pairs and there is 10 cards left to pick from and then the 6 because you need 6 more cards to make 12 after the three pairs. and the 4C1*6 is for the suit of the remanding 6 cards

zarkon · Answer

yes...there are 10 types of cards left over and we want 6 of them.   then pick one card from each of these 6 groups

zarkon · Answer

note it is (4C1)^6 not 4c1*6

anonymous · Answer

I just need a more detailed explanation please