General Holdem Probability Question

[BogusPomp]

Most everyone knows the chance of being dealt any pair pre-flop in Holdem is 1/17 (or 16 to 1).

I was wondering, more generally...

At an 'N' person table, what are the chances 'K' players will be dealt a pair before the flop??

Thanks for any help

[BogusPomp]

More specifically, does this example qualify as a Bernoulli trial with p= 1/17?

[AaronBrown]

Almost, but not quite. The reason is the events are not quite independent. For the first player, there are 78 pairs in the deck and 52*51/2 possible hands. 78/(52*51/2) = 1/17.

For the second player, there are 50*49/2 hands left in the deck. If the first player got a pair, there are 73 pairs left. If the first player didn't get a pair, there are 72.

It's not hard to compute the distribution of pairs for N players using a spreadsheet, but there's no simple formula to write down.