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Probability question

Four people are playing a game of cards in which they each receive 13 cards.

What is the probability that in a given deal one player receives two aces, one player receives no aces and the other 2 players have once ace each?
Original post by stealth_writer
Four people are playing a game of cards in which they each receive 13 cards.

What is the probability that in a given deal one player receives two aces, one player receives no aces and the other 2 players have once ace each?


What have you done/tried, and what are your thoughts?
Original post by ghostwalker
What have you done/tried, and what are your thoughts?


Well I've tried a massive tree diagram and drank three cans of red bull to help sustain my efforts. But still no clue. Could you help me please mate? cheers
Original post by stealth_writer
Well I've tried a massive tree diagram and drank three cans of red bull to help sustain my efforts. But still no clue. Could you help me please mate? cheers


Clue: You want to work with combinatorics, and consider how many ways you can arrive at a deal that meets your criterion, and how many deals there are without any restrictions. The ratio of the two gives you your probability.

I think that's the easiest way.
(edited 10 years ago)
Original post by ghostwalker
Clue: You want to work with combinatorics, and consider how many ways you can arrive at a deal that meets your criterion, and how many deals there are without any restrictions. The ratio of the two gives you your probability.

I think that's the easiest way.


The only bit i am struggling with- how many different ways are there to distribute the four aces at a deal that satisfies the criteria in the question exactly? Please could show me how many different ways to there are to distribute the 4 aces as desired in the Q? I should be ok from after that. Thanks
Original post by stealth_writer
The only bit i am struggling with- how many different ways are there to distribute the four aces at a deal that satisfies the criteria in the question exactly? Please could show me how many different ways to there are to distribute the 4 aces as desired in the Q? I should be ok from after that. Thanks


You could start by distributing 3 aces, so you have 1,1,1,0 - how many ways?

Then distribute the 4th ace to a hand that already has one - how many ways?

I confess to being lost as to how you're actually doing it, but the above should lead you to the answer to the bit you're struggling with.

Edit: Depending on how you're doing it, you may just be looking for the number of arrangements of 2,1,1,0, which would just be 4!/2!
(edited 10 years ago)

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