Probability of trips on flop

[Supern]

10 players at the table.
Flop is JJA.

1. What is the probability that 0 players have been dealt a J?

2. What is the probability that 1 player have been dealt a J?

3. What is the probability that 2 players have been dealt a J?

4. What are the probabilities when there are 9, 8, 7 and 6 players around the table instead?

I don't care about if they are playing the cards or not. Just the dealt probablities.

Obviously if the flop is KK3 it is more probable someone has trips (and are in the game) than if the flop is 33K. /images/graemlins/smile.gif

[Supern]

No one knows this?

[lossage]

[ QUOTE ]
10 players at the table... Flop is JJA.

1. What is the probability that 0 players have been dealt a J?

[/ QUOTE ]

There are 49 cards left for people to be dealt. There are C(49,20) sets of cards that could be dealt to players. C(47,20) of those sets contain neither of the remaining jacks. Therefore, the probability that nobody has a jack is: C(47,20)/C(49,20) = 0.345.

For nine players, it's: C(47,18)/C(49,18) = 0.395. For eight, C(47,16)/C(49,16) = 0.449.

Hopefully, this will help get you started.