# Statistics problem... 10 points reward for help....?

A lottery has 70 numbers (1-70). From this set, each week 20 numbers are chosen on a random basis corresponding to the winning numbers. Any player that plays the lottery has then a choice to bet on 1 to 11 numbers. If the numbers chosen by the player correspond to the 20 drawn numbers, the player can win a prize. Therefore the least requirement for winning is one match and the most 11 matches.

With the given information above:

a) What is the probability for the player to win money if he bets on only one number, two numbers, three numbers, and so on ..., until all eleven numbers.

b) What is the probability to at least win something.

PLEASE SHOW ALL THE STEPS and describe your thinking if possible... Thanks guys...

Relevance

If the player bets on one number, the probability to win is the probability to have 19 numbers among 69 :

it's 69C19 / 70C20 = 2/7

If he bets on two numbers, if he wins then we have to choose the others 18 good numbers among the 68 not choosed by the player : the probability to win is 68C18 / 70C20 = 20*19 / 70*69 = 38/483

and so on ...

If he bets on n numbers, the probability he wins is

(70-n)C(20-n) / 70C20 = [20*19*...*(20-n+1)] / [70*69*...*(70-n+1)]

for n=11, it's equal to 7.7 * 10^{-8}