STAT poker questions:

1. Find the probability of 2 triples and 2 pairs (e.g. KKKQQQ2255) in a 10 card poker hand.

2. Suppose 5 cards of a poker hand are dealt one at a time without replacement. If the first two cards drawn are aces, what is the probability two of the last three will be aces?

Question

STAT poker questions:

1. Find the probability of 2 triples and 2 pairs (e.g. KKKQQQ2255) in a 10 card poker hand.

2. Suppose 5 cards of a poker hand are dealt one at a time without replacement. If the first two cards drawn are aces, what is the probability two of the last three will be aces?

zarkon · Answer

where are you stuck...you have any ideas?

anonymous · Answer

For the first one, I know I'm supposed to go with $$\left(\begin{matrix}52 \ 10\end{matrix}\right)$$ as my denominator

anonymous · Answer

Unsure about the rest

zarkon · Answer

you need to choose the types of cards to be your triples  and choose the type of cards to be your doubles

do you know how to do this?

zarkon · Answer

$${13 \choose 2}{4 \choose 3}{4 \choose 3}{11 \choose 2}{4 \choose 2}{4 \choose 2}$$

anonymous · Answer

could you please explain why you did that.

zarkon · Answer

there are 13 types of cards (2 through Ace).  Choose 2 to be the two triples.  then from the first group of 4 cards choose 3 and from the second group choose 3.  You now have your two triples.  Now there are only 11 types of cards left...go through the same process.