Game of Keno: What is the percent chance that a player selects exactly 3 winning numbers? In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to 80. A win occurs if the player has correctly selected 3,4, or 5 of the 20 winning numbers. May anyone give me a hint to solve this problem, please? Thanks!

The number of ways to select 20 out of 80 is $\binom{80}{20}$. The player needs to select 3,4, or 5 of these AND the rest from the remaining 60 numbers: $\binom{20}{3} \times \binom{60}{17} + \binom{20}{4} \times \binom{60}{16} +\binom{20}{5} \times \binom{60}{15}$. Can you sort out the rest?