# Lottery question

#### 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

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#### 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

eldrick said:
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?

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