def array_permutations array, index=0
  # index is 0 by default : start at the beginning, more elegant.
  return array[-1] if index == array.size - 1 # Return last element if at end.
  result = []
  array[index].each do |element| # For each array
    array_permutations(array, index + 1).each do |x| # Permute permute permute
      result << "#{element}, #{x}"
    end
  end
  return result
end

So, we get this:

first = ['one', 'two']
second = ['three', 'four']
third = 'five', 'six']
result = array_permutations [first, second, third]
=> ["one, three, five", "one, three, six", "one, four, five", "one, four, six", "two, three, five", "two, thre
e, six", "two, four, five", "two, four, six"]

Magic!

——
Edit – of course, my solution is hackish, and someone came up with a quicker and more elegant solution:

def fancy_array_permutation array
  return array[0] if array.size == 1
  first = array.shift
  return first.product( fancy_array_permutation(array) ).map {|x| x.flatten.join(" ")}
end

This gives the same result as above.