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
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