Win $20,000: Calculating the Odds of Lottery Ticket Prizes

[eldrick]

there is an interesting show I've caught on satellite which is based on a domestic lottery

you are given the choice of having 100,000 lottery tickets or a $20,000 cash prize

now to simplify, the odds of matching 3 balls out of 6 is

~ 1 in 56.6

& the prize for matching 3 balls is $10

if you used a rough calculation, you are likely to win ( just considering 3 balls )

100,000 *( 1/56.6)* 10 =

$17,660

if you took the option of 100,000 tickets


now, I'm asking what are the precise odds of winning $20,000 ( 2,000 winning "3 ball" tickets ) ?

i believe it may be something along the lines of


( (1/56.6) ^ 2000 ) * (55.6/56.6) ^98000 ) * no. of ways you can ?permute/ ? combine 2000 draws amongst 100,000


any help would be gratefully appreciated

 

[juvenal]

That looks right - the binomial term for 2000 successes where the probability p is 1/56.6, normalized by the total number of possibilities.

 

[Townsend]

now to simplify, the odds of matching 3 balls out of 6 is

~ 1 in 56.6

I don't get it? Why not 6 choose 3 ways of selecting 3 balls from 6 giving you odds of 1:19?