Keno odds of picking 11+ numbers if 20 total are selected out of 80 In the game of keno, there are a set number of balls in the spinner, in this case, 80. They are numbered 1-80. The goal is to guess the numbers that will be selected at random. In this particular keno variant, you are allowed to pick 20 numbers. What are the odds that you will get more than 10 correct (order does not matter)? (11-20)

The chance of getting exactly eleven is $\frac {{20 \choose 11}{60 \choose 9}}{80 \choose 20}$ where the $20 \choose 11$ is the number of ways to pick the winning balls out of your $20$, the $60 \choose 9$ chooses the balls drawn that you did not pick, and the $80 \choose 20$ chooses the winning balls from all balls. You should be able to do higher numbers by analogy, then add them all up to get the total probability. Alpha finds\(60%20choose%2020-n\)%2F\(80%20choose%2020\)%20from%2011%20to%2020) a total probability of about $0.0008$, almost all of which comes from hitting $11$ or $12$.