What are the odds of, in a set of X people, there being at least Y people who share a birthday?

Birthday Collisions.rb

# Thomas Shaddox
# https://github.com/baddox
# Assumes birthdays are independent (i.e. uniformly distributed)
days = 365
ppl = 290 # I'm so popular
trials = 10_000
at_least_four = 0

trials.times do
  array = [0] * days
  ppl.times do
    day = (rand() * days).truncate
    array[day] += 1
  end
  at_least_four += 1 if array.max >= 4
end

puts "Probability of at least 4 shared birthdays is #{(at_least_four / trials.to_f) * 100}%"