Probability in Keno I've been trying to figure this out for a while now. In keno, 20 different numbers between 1 and 80 are chosen. I then choose 5 numbers between 1 and 80. What is the chance that those 20 numbers contain the 5 numbers I chose? I tried to solve this by factoring it first: 5 in 80 is 1 in 16, 20 in 80 is 4 in 16. This means that there must be a 1 in 4 chance that one of my numbers will be in the 20 chosen. So for all 5, I just said 1/(4^5) which is 1/1024. But this is not right. How could I calculate the correct answer?

The number of ways to select five numbers out of twenty is $\binom {20}5$ and the number of ways to select five out of eighty is $\binom {80}5$, so your chance of winning is $\frac {\binom {20}5}{\binom {80}5}=\frac {20!}{15!}\cdot \frac {75!}{80!}=\frac {51}{79079}\approx 0.000645$