[SittingBull]

have a scientific calculator,use the combination formula:
nCr=n!/r!(n-r)!
n!=n(n-1)(n-2)(n-3)...1
Example:
5!=5(5-1)(5-2)(5-3)(5-4)=5(4)(3)(2)(1)=120
Example;
compute 6C4
Ans
6C4=6!/4!(6-4)!
6!=6(6-1)(6-2)(6-3)(6-4)(6-5)=6*5*4*3*2*1=720


If U have a scientific calculator,U will usually see nCr
on the calculator.
nCr means that the order is not important.
For example,a selection of Ac,9h,2d is the same as the selection 2d,Ac,9h.
Let's assume U want to find out how many ways of choosing 2 K's from a deck of 52 .
There are 4 K's in the deck--Kc,Kh,Ks,Kd
Ans:
4C2=4!/2!(4-2)! = 4*3*2*1/2*1*2!=4*3*2*1/2*1*2*1=6
Note that Kc,Kh and Kh,Kc is the same selection--so U just count it as 1 selection.
The order is not important--just the selection.
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The probability of any event occurring is the total # of favorable outcomes/total # of outcomes
Example for the 4-flush problem

Since U have 2 of the 13 suits,there are 11 of your suits remaining.
The # of DIFFERENT ways of selecting 2 of the remaining 11 suits is given by 11C2=11!/2!(11-2)!
These selections are all favorable to your oucome.
If U subtract the 13 suits from the total # of cards in the deck,52,then there will be 39 of these that are non - suited of your type of suit. 11C2 gives U the # of ways of flopping two different suits ,that is ,two of your suit. But there is a 3rd card to complete the flop.
So for each way of selection 2 of your suited cards from the 11 that are suited,there are 39C1 ways of selecting the remaining one non-suited card to complete the flop.
Hence,U will have a favorable flop 11C2*39C1 times.
These are your favorable outcomes.
Since U have 2 cards in your hand,there are 50 unseen cards.
U can select 3 of these 50 unseen cards 50C3 different ways.
These are BOTH favorable and unfavorable outcomes(the total # of different outcomes)
The probability=total # of favorable outcomes/total # of both favorable and unfavorable outcomes.
So Probability=11C2*39C1/50C3 for a 4-flush flop.
Happy Poering, [img]/forums/images/icons/laugh.gif[/img]
SittingBull