input: ### Instruction:
  Write a function in Python that determines if a list of words can be used to form a given target word by using each word at most once, and returns the number of ways to achieve this.
  
  ### Input:
  ["cat", "dog", "cat", "bat"]
  "catdog"
  
  ### Output:
  Write a function to determine if a list of words can be used to form the given target word by using each word at most once, and return the number of ways to do this.
  
  def count_ways_to_form_word(words, target):
      from collections import Counter
      
      def helper(i):
          if i == len(target):
              return 1
          if i > len(target):
              return 0
          count = 0
          for word in words:
              if target[i:i+len(word)] == word:
                  count += helper(i + len(word))
          return count
      
      words_counter = Counter(words)
      return helper(0)
  
  assert count_ways_to_form_word(["cat", "dog", "cat", "bat"], "catdog") == 2
output:     from collections import Counter
      
      def helper(i, used_words):
          if i == len(target):
              return 1
          if i > len(target):
              return 0
          count = 0
          for word in words_counter:
              if words_counter[word] > used_words.get(word, 0) and target[i:i+len(word)] == word:
                  used_words[word] = used_words.get(word, 0) + 1
                  count += helper(i + len(word), used_words)
                  used_words[word] -= 1
          return count
      
      words_counter = Counter(words)
      return helper(0, {})