#math - Mon 12 Mar 2007 between 01:34 and 01:52

clarity_given 52 cards with 13 values and 4 suits... how many possible sets
of 3 cards of the same suit are there
majdTRWBW, ok, thanks
clarity_is it 4*13*12*11 ?
clarity_: not unless you count the order of the cards
clarity_since there's 13*12*11 different ways to pull 3 cards of the same suit... then there's 4 different suits?
TRWBWclarity_: set means no order, so you need to divide by 3!
bungTRWBW, ok i think i can grasp the function you've written, is that something general for halfturns?
majdaaaaah i get itt...so partial derivative is the derivative parallel to a plane, gradient is the derivative in any direction...
clarity_so 13*12*11/3*2 ?
them times 4?
i'm not sure where the 3! is coming from?
do you care to explain
TRWBWmajd: the neat think is that a vector + dot product captures it. that's what makes it all worthwhile. you might guess that you have to differentiate in any possible direction, but it turns out if you do it in just 3 directions, you capture all the others.
clarity_: forget suits, how many ways can you pick a set of 3 letters?
clarity_ah... n choose k = n!/k!(n - k)!
3 letters given 13?
TRWBWclarity_: sure or 26 whatever
clarity_: but i think you got it
mysteryxdoes anyone here know rf theory...?
clarity_26*25*24 I believe
26 possiblities then 25 then 24
but that's including order
TRWBWclarity_: nope, that's words, not sets. setwise {'c','a','t'} is the same as {'a','c','t'}
majdTRWBW, yeah that's pretty cool
TRWBWclarity_: that's where the 3! come from
so you're counting all the permutations of the set... so if it's 3 elements you're counting 3! permutations
so dividing by 3! would give you the one set
TRWBWclarity_: yeah, it's 4*13*12*11/3!
clarity_: if it was 6 cards, it would be 4*13*12*11*10*9*8/6!
clarity_awesome! I've been having a lot of trouble trying to figure out why there's k! and it makes sense now...
i think
okay... 52 cards 13 values 4 suits. sets of 3 cards with the first 2 suits different from the 3rd is: 4*(13*12*39/3!) since 52 - 13 = 39
TRWBWclarity_: pick the 3rd first.
clarity_hrm 4*((13*12/2!)*(39/1!))
cldfor a condition like h(x,y,z) = 0 where y and z are functions of x, what do i need in order to make claims about the uniqueness of solutions z(x), given the function f(x)?

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