Probability of 3card flush and 2 card flush from 5 cards

Question

Got a question I can't quite wrap my head around.

I would like to know the probability of getting a 3 card flush out of 5 cards and having the other 2 cards be a flush of a different suit.

I think it should look something like (13C3 x 4C1 x (not sure)) x (13C2 x 3C2 x (not sure)) / 52C5

Really i'm just lost here lol.

paparazzo · Accepted Answer · 2016-10-19 17:51:56Z

1

13C3 x 4C1 x 13C2 x 3C1 / 52C5 = 0.103
8.7 : 1

answered Oct 16 '16 at 10:14

paparazzo

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But doesn't 13C3 x 4C1 give us the chance of getting a 3 card flush using only 3 cards? Wouldn't we multiply this by 5C3 for example? – freshbooze Oct 16 '16 at 10:25
Buy you are looking for the chance of 3 card flush using only 3 cards? – paparazzo Oct 16 '16 at 10:32
But we don't know which 3 of the 5 cards we will use though? Like we could use cards 123 or 124 or 125 or 234 etc. If we compare 13C3 4c1 with 15C5 4c1 it shows that the odds of getting a 5card flush is higher than a 3card, which is obviously wrong. Or am i wrong lol – freshbooze Oct 16 '16 at 11:20
The order of the cards does not matter. I suggest you read up on subject. – paparazzo Oct 16 '16 at 11:26
Will do. I'm pretty sure I understand now. Just as a confirmation, the probability of getting a 3card flush with 3 cards only would be, 13c3 4c1 / 52c3 yes? – freshbooze Oct 16 '16 at 12:28

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