flop scenarios

[cowl]

What is the total number of flop scenarios? and what is the right way to figure it out? If you go with 50 choose 3 it gives you 19600. But if you go with 50*49*48 it gives you 117600.
Am I totally missing the 50 choose 3 concept here because these two ways have a pretty big difference. Any help here is appreciated.

[BruceZ]

[ QUOTE ]
What is the total number of flop scenarios? and what is the right way to figure it out? If you go with 50 choose 3 it gives you 19600. But if you go with 50*49*48 it gives you 117600.
Am I totally missing the 50 choose 3 concept here because these two ways have a pretty big difference. Any help here is appreciated.

[/ QUOTE ]

It depends on whether the order of the cards matters. If order doesn't matter, for example if you consider As Ks Qs to be the same flop as Qs Ks As, then the correct answer with 50 remaining cards is 50 choose 3, also written as C(50,3), and this is equal to 50*49*48/(3*2*1) = 19,600. This is called the number of combinations. If the order does matter, then the answer is 50*49*48 = 117,600. This is called the number of permutations, and is denoted P(50,3). Notice that there are 6 times as many permutations as combinations because for each combination, there are 6 ways to order the 3 cards. The number of ways to order 3 cards is 3 factorial, written 3!, which is equal to 3*2*1 = 6. In general, the number of ways arrange k cards is k!, so the relationship between combinations and permutations is given by C(n,k) = P(n,k)/k!

[cowl]

thanks [img]/images/graemlins/smile.gif[/img]