# Birthday.rb -- happy bday to EY employees everywhere
# with love from san diego :p, David Salamon 2008

def no_shared_birthdays_for(people, days=365)
  return 1.0 if people == 0
  return ((days - 1.0) / 365) * no_shared_birthdays_for(people - 1, days - 1)
end

puts "Section one... how unlikely are collisions with different employee head counts?"
(2..60).each {|e| puts " - with #{e} employees : #{1.0 - no_shared_birthdays_for(e)}" }


def choose(n, m)
  m = n - m if m < n - m
  accumulator = 1.0
  (n-m).times {|i| accumulator *= (m + i + 1) }
  (n-m).times {|i| accumulator /= (i + 1)}
  accumulator.to_i
end

def shared_birthdays_for(people, days=365)
  return 1 if people == 0 || people == 1
  return (1.0/days) * shared_birthdays_for(people-1, days)
end

$employee_count = 50
(2..10).each {|e|
  chance = choose($employee_count, e) * shared_birthdays_for(e) * no_shared_birthdays_for($employee_count - e)
  puts "chance of *exactly* #{e} people sharing a birthday: #{chance}"
}