OT Test[ing again] - No need to reply

[Klaus-Peter Schrage]

Kurt Wall wrote:
> Quoth Klaus-Peter Schrage:
> 
>>Tom Wilson wrote:
>>
>>>Here in America, many states have what they call a Lotto.  What happens
>>>is you go to a local convenience store and purchase a Lotto ticket for a
>>>US $1 a ticket.  They usually have 6 numbers on them from 1 to 40 or
>>>so.  Then once a week they draw numbers out of a contraption that has a
>>>bunch of numbered ping pong balls in it and you hope that the six you
>>>picked (or had randomly generated) on your ticket are the same six that
>>>pop up out of the ball machine.  Is so you win the jackpot of generally
>>>some tens to hundreds of millions of dollars.  
>>>
>>>Most people don't win.  Thus you have to pretty lucky if you do. 
>>>
>>
>>The chances of winning aren't that bad: 1:3838380
> 
> 
> Mm, my statistics is a little rusty, but wouldn't the chances be rather
> worse? Order matters, so we want permutations, not combinations. So,
> 
> 40_P_6 = 40!/(40 - 6)! = 40!/34! = 2,763,633,000
> 40_C_6 = 40!/(6! * (40 - 6)!) = 40!/(6! * 34!) = 3,838,380
> 

I don't know about the details of the American lotto system, but 
according to Tom's description it seems to be similar to our's (apart 
from us having numbers from 1 to 49). Thus, order doesn't matter: a 
sequence of drawings of ping pong balls like 2, 4, 39, 5, 40, 9 yields 
the same result as 40, 2, 39, 5, 9, 4 or any other permution. So, it's 
combinations.
Klaus