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I am trying to calculate probability if 3 card Indian poker is being played between 8 players drawing 3 cards each what are chances that at least one player has either flush or straight or royal flush

if 8 players drawing 3 cards each chances that at least one (or even more than 1 ) has flush or straight or royal flush

it will be p(f) = p (a) + p(b) - p(a, b), and so on for multiple players

total chances of single player having flush is , 13 of same suits nCr ~ 13C4 = 1144 -48 (royal flush ) = 1096 1096/22100 = 4.96%

I want to extend this for multiple players, can you suggest how do I calculate for 8 players.

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