Dinner Reservations Experience shows that $20\%$ of the people reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes $52$ reservations, then what is the probability that it will be able to accommodate everyone?
My understanding: If the reservation is $52,$ and $20\%$ people don't show up, would not the probability of accommodating every one be $1$?

Given that a table that has been reserved will be taken by a party who reserved it is $80\%$, the probability that the restaurant accommodates everyone is 
$$1 - \Pr[52\ \ \mbox{parties show up}]  - \Pr[51\ \mbox{parties show up}],$$ 
where probability that $k$ out of $52$ parties show up is
$$\Pr[k\ \mbox{parties show up}] = \binom{52}{k}0.8^{k}(1-0.8)^{52-k}.$$
