Permutation vs Combination

[limhuisi]

Hi David,

I am recently trying to apply this simple math rule (high school) into the lottery.
In SG, we have a lottery totalling to SG8mio...
and the lottery is in 6 digit.
Out of 10 possible numbers, 1,2,3,4,5,6,7,8,9,0 ,
it seems like I just need to use 10C6=210 combination to buy a ticket worth SG0.50=SG105 to win that SG8mio...
Doesn't it seems attrative to buy? but somehow I think I am misssing something here...if everyone is to do that, there will be millionaire around dy right?

What am I missing here?

Regards,
Hui Si

P/S: I know this have nothing to do with FRM, but suddenly I was thinking that maybe striking that lottery is much more easier than study for FRM...haha..

 

[David Harper CFA FRM]

Hi Hui,

Hmmm...i must be dense because i don't disagree. Combination implicity assumes "Without replacement" so your 10C6 excludes results like "1 2 2 3 4 5" because 2 can't appear twice? If that's true, I agree that are 210 combinations. (further, order does not matter of course). Even so, "with replacement" the upper limit is still only 10^6 or 10 million.

I conclude, with all due respect to you, that perhaps this does not capture the rules?

Or, we are both on the wrong course (you taking FRM, me teaching same) and we should immediately redirect our efforts to this lottery. This indeed seems to a much faster path finanical well-being!

David

 

[David Harper CFA FRM]

...or if order *does* matter, 10permutation6 = 151,200. I don't recognize your payoff units so i don't know if that resolves? David