ssho88
Joined: Oct 16, 2011
• Posts: 502
November 2nd, 2020 at 4:01:49 AM permalink
Quote: billryan

Thank you for your efforts.

5 cards poker hand with 4 suits, but there are 2 cards with same suit, so total different permutations = 5!/2!.

So, probability = 13/52 * 13 /51 * 13/50 * 13/49 * 48/48 * 5!/2! = 0.2637455.
malgorium
Joined: Aug 14, 2013
• Posts: 60
November 2nd, 2020 at 3:36:33 PM permalink
Quote: ssho88

5 cards poker hand with 4 suits, but there are 2 cards with same suit, so total different permutations = 5!/2!.

So, probability = 13/52 * 13 /51 * 13/50 * 13/49 * 48/48 * 5!/2! = 0.2637455.

Ah interesting. Yea, I did it like

If you want all 4 suits, then there have to be exactly 2 of 1 suit. So there are 13C2 ways to do that and 13C1 for the other suits. But the double-suit can happen for any of the 4 suits, so there are 4(13C2)(13C1)(13C1)(13C1) total ways to make a hand with all 4 suits.

And there are 52C5 total ways to make any 5 card hand, so the total probability is just the quotient of the two, which is the same value you got.

That's the great thing about math - more than 1 way to skin a cat!
marcel55
Joined: Feb 21, 2021
• Posts: 18
March 20th, 2021 at 7:19:39 AM permalink
Did you do all the calculation again?
Mission146
Joined: May 15, 2012
• Posts: 13201
March 20th, 2021 at 8:48:17 AM permalink
Quote: malgorium

Ah interesting. Yea, I did it like

If you want all 4 suits, then there have to be exactly 2 of 1 suit. So there are 13C2 ways to do that and 13C1 for the other suits. But the double-suit can happen for any of the 4 suits, so there are 4(13C2)(13C1)(13C1)(13C1) total ways to make a hand with all 4 suits.

And there are 52C5 total ways to make any 5 card hand, so the total probability is just the quotient of the two, which is the same value you got.

That's the great thing about math - more than 1 way to skin a cat!

Here's another way:

nCr(13,2)*nCr(13,1)*nCr(13,1)*nCr(13,1)/nCr(52,5) = 0.0659363745498199

0.0659363745498199 * 4 (suits) = 0.2637454981992796 (Difference with SSho due to rounding)

Which is actually the same way you did it, essentially, just using the nCr function instead.
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