How many ways can the letters in australia be arranged so that ONLY 2 A's are together?

gistfile1.rb

# This generates all combinations of words with the letters in 'australia', 
# and then filters down to include only words with two consequtive "a"s 
# and then excludes any words with 3 consecutive "a"s, leaving the words with only 2 a's together.
#
# Answer: 30240

class String
  def each_char_with_index
    0.upto(size - 1) do |index|
      yield(self[index..index], index)
    end
  end
  def remove_char_at(index)
    return self[1..-1] if index == 0
    self[0..(index-1)] + self[(index+1)..-1]
  end
end

@arr = Array.new
def permute(str, prefix = '')
  if str.size == 0
    @arr << prefix
    return
  end
  str.each_char_with_index do |char, index|
    permute(str.remove_char_at(index), prefix + char)
  end
end

permute("australia")
@arr.find_all{|t| t.include?("aa")}.reject{|t| t.include?("aaa")}.uniq.length