Question

The public transport system is aware that one person in twenty does not buy a ticket for their trip. The manager decides to challenge 200 travelling people as to charger they have a valid ticket or not. (a) calculate the probabilty that everyone had a ticket, (b) calculate the probabilty that at most 3 people had no ticket, and (c) calculate the probabilty that between 7 and 14 (inclusive) had no ticket. I thought binomial? But then 200 is too big for it? Thanks for any help!