If I have 5 groups called a,b,c,d,e. And I randomly assign these five groups to 20 people. What is the odds that there will be 4 people in each group?

Or more specificially how many times do I have perform this cacluation until there are exactly 4 people in each group?

What then is the odds if I have 20 different dates. So 20 people and 20 dates how many times will I have to perform that calculation to get exactly 4 people in each group on each day.