Up to this point correct. There are 56 orderless combinations.
Ordered actually, you could have L1 and L2 and that combinations lets you know in what order they are. There's 28 orderless combinations. Still if you're doing both of them ordered it doesn't affect the math.
There are 6 F cards. How many 3-card orderless combinations? 6x5x4 / 3x2x1 =20.
So out of 56 combinations 20 involve FFF.
or 28 & 10 (divided by half
), which we both agree on. The 20 throws me off but i can see how it goes together.
Not sure what you're doing next. Can you explain.
Well i WAS
just doing the raw combinations using 5 remaining cards and ignoring the order of the L's, but i see that was wrong. Thus x3 fixes those (and adding to 28 confirms it
Probability of drawing first F is 6/8
Second is 5/7 since 7 cards are left with 5 F.
Third is 4/6.
Probability of first 3 being f is 6/8 x 5/7 x 4/6 = 20/56.
With programming, blundering through sometimes until you get the proper answer is how it works :P Been developing a method of figuring out these combinations to do data compression.
I suppose my lack of Algebra makes me feel like a dunce here.